Abstract: In this talk, I will discuss the relationship between kernel methods and (two-layer) neural networks for generalization, which aims to theoretically understand the separation from the perspective of function spaces. First, I will start with random features models (a typical two-layer neural network, also a kernel method) from under-parameterized regime to over-parameterized regime, which recovers the double descent and demonstrates the benefits behind over-parameterization. Second, I will compare kernel methods and neural networks via random features from reproducing kernel Hilbert space (RKHS) to Barron space, which leaves an open question: what is the suitable function space of neural networks?

by Professor Terry Lyons, University of Oxford

by Professor Anastasia Papavasiliou

by Professor Geoff Nicholls, University of Oxford

Professor Jim Smith

by Professor Gareth Roberts

I was asked to consider the available data on Covid-19 patients' path into hospital, and then to intensive care, or death, or transfer or discharge. Of course, once in intensive care, patients can move to the states death, discharge home, discharge to nursing home, discharge to hospital ward. I was invited by those who think I know about analysis of times to events with messy data. The data is messy, and there are other challenges.

I benefited from conversations with medical friends and colleagues, particularly a respiratory physician.

Depending on permissions, I will either illustrate issues with artificial data, or present actual results.

Speaker: Gabriel Peyré, CNRS and Ecole Normale Supérieure

Speaker: Sofia Olhede

Localizing Changes in High-Dimensional Vector Autoregressive Processes

Dr. Pauline O'Shaughnessy, University of Wollongong, Australia

Title: Bootstrap inference in the longitudinal data with multiple sources of variation

Abstract: Linear mixed models allow us to model the dependence among the responses by incorporating random effects. Such dependence inherent in the longitudinal data from a complex design can be from the clustering between subjects and the repeated measurements within the subject. When the underlying distribution is not fully specified, we consider a class of estimators defined by the Gaussian quasi-likelihood for normal-like response variable. Historically it is challenging to make inference about the variance components in the framework of mixed models. We propose a new weighted estimating equation bootstrap, which varies weight schemes for different parameter estimators. The performance of the weighted estimating equation bootstrap is empirically evaluated in the simulation studies, showing improved coverage and variance estimation for the variance component estimators under models with normal and non-normal distributions for random effects. The asymptotic properties will also be addressed and we apply this new bootstrap method to a longitudinal dataset in biology.

(This is a joint work with Professor Alan Welsh from the Australian National University.)

Prof. Malgorzata Bogdan, University of Wroclaw, Poland (15:00-16:00)

Abstract: Sorted L-One Penalized Estimator is a relatively new convex optimization procedure for identifying predictors in large data bases.
In this lecture we will present the method, some theoretical and empirical results illustrating its properties and the applications in the context of genomic and medical data. Apart from the classical version of SLOPE we will also discuss its spike and slab version, aimed at reducing the bias of estimators of regression coefficients. When discussing SLOPE we will also present some new theoretical results on the probability of discovering the true model by LASSO (which is a specific instance of
SLOPE) and its thresholded version.

Prof. Karla Hemming, University of Birmingham, UK (15:00-16:00)

Speaker: Clair Barnes, University College London, UK

Death & the Spider: postprocessing multi-ensemble weather forecasts with uncertainty quantification

Ensemble weather forecasts often under-represent uncertainty, leading to overconfidence in their predictions. Multi-model forecasts combining several individual ensembles have been shown to display greater skill than single-ensemble forecasts in predicting temperatures, but tend to retain some bias in their joint predictions. Established postprocessing techniques are able to correct bias and calibration issues in univariate forecasts, but are generally not designed to handle multivariate forecasts (of several variables or at several locations, say) without separate specification of the structure of the inter-variable dependence.

We propose a flexible multivariate Bayesian postprocessing framework, developed around a directed acyclic graph representing the relationships between the ensembles and the observed weather. The posterior forecast is inferred from the ensemble forecasts and an estimate of their shared discrepancy, which is obtained from a collection of past forecast-observation pairs. The approach is illustrated with an application to forecasts of UK surface temperatures during the winter period from 2007-2013.

Speaker: Karla Hemming, University of Birmingham (1500-1600)

The I-squared-CRT statistic to describe treatment effect heterogeneity in cluster randomized trials.

K Hemming (Birmingham) and A Forbes (Monash)

Treatment effect heterogeneity is commonly investigated in meta-analyses of treatment effects across different studies. The effect of a treatment might also vary across clusters in a cluster randomized trial, and it can be of interest to explore this at the analysis stage. In stepped-wedge designs and other cluster randomized designs, in which clusters are exposed to both treatment and control conditions, this treatment effect heterogeneity can be identified. When conducting a meta-analysis it is common to describe the magnitude of any treatment effect heterogeneity using the I-squared statistic, which is an intuitive and easily understood concept. Here we derive and evaluate a comparable measure of the description of the magnitude of heterogeneity in treatment effects across clusters in cluster randomized trials, the I-squared-CRT.

Dr. Yoav Zemel, University of Göttingen, Germany (15:00-16:00)

Title: Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

Abstract: Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in contexts where multiple functional populations are to be compared. Statistical techniques to analyse such variation are intimately linked with the choice of metric on covariance operators, and the intrinsic infinite-dimensionality of these operators. We describe the manifold-like geometry of the space of trace-class infinite-dimensional covariance operators and associated key statistical properties, under the recently proposed infinite-dimensional version of the Procrustes metric (Pigoli et al. Biometrika 101, 409–422, 2014). We identify this space with that of centred Gaussian processes equipped with the Wasserstein metric of optimal transportation. The identification allows us to provide a detailed description of those aspects of this manifold-like geometry that are important in terms of statistical inference; to establish key properties of the Fréchet mean of a random sample of covariances; and to define generative models that are canonical for such metrics and link with the problem of registration of warped functional data.

Prof. Renauld Lambiote, University of Oxford, UK (15:00-16:00)

Higher-Order Networks:

Network science provides powerful analytical and computational methods to describe the behaviour of complex systems. From a networks viewpoint, the system is seen as a collection of elements interacting through pairwise connections. Canonical examples include social networks, neuronal networks or the Web. Importantly, elements often interact directly with a relatively small number of other elements, while they may influence large parts of the system indirectly via chains of direct interactions. In other words, networks allow for a sparse architecture together with global connectivity. Compared with mean-field approaches, network models often have greater explanatory power because they account for the non-random topologies of real-life systems. However, new forms of high-dimensional and time-resolved data have now also shed light on the limitations of these models. In this talk, I will review recent advances in the development of higher-order network models, which account for different types of higher-order dependencies in complex data. Those include temporal networks, where the network is itself a dynamical entity and higher-order Markov models, where chains of interactions are more than a combination of links.

Speaker: Dr. Ben Calderhead, Department of Mathematics, Imperial College London
Title: Quasi Markov Chain Monte Carlo Methods

Abstract: Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior densities within the Bayesian framework, in particular for inverse problems. We introduce a general parallel Markov chain Monte Carlo(MCMC) framework, for which we prove a law of large numbers and a central limit theorem. In that context, non-reversible transitions are investigated. We then extend this approach to the use of adaptive kernels and state conditions, under which ergodicity holds. As a further extension, an importance sampling estimator is derived, for which asymptotic unbiasedness is proven. We consider the use of completely uniformly distributed (CUD) numbers within the above mentioned algorithms, which leads to a general parallel quasi-MCMC (QMCMC) methodology. We prove consistency of the resulting estimators and demonstrate numerically that this approach scales close to n^{-2} as we increase parallelisation, instead of the usual n^{-1} that is typical of standard MCMC algorithms. In practical statistical models we observe multiple orders of magnitude improvement compared with pseudo-random methods.

Daniel Rudolf, Institute for Mathematical Stochastics, Georg-August-Universität Göttingen

Title: Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling

Abstract: By proving Wasserstein contraction of simple slice sampling for approximate sampling of distributions determined by log-concave rotational invariant unnormalized densities we derive an explicit quantitative lower bound of the spectral gap. In particular, the lower bound of the spectral gap carries over to more general distributions depending only on the volume of the (super-)level sets of the unnormalized density.

Speaker: Spencer Wheatley, ETH Zurich, Switzerland

Title: The "endo-exo" problem in financial market price fluctuations, & the ARMA point process

The "endo-exo" problem -- i.e., decomposing system activity into exogenous and endogenous parts -- lies at the heart of statistical identification in many fields of science. E.g., consider the problem of determining if an earthquake is a mainshock or aftershock, or if a surge in the popularity of a youtube video is because it is "going viral", or simply due to high activity across the platform. Solution of this problem is often plagued by spurious inference (namely false strong interaction) due to neglect of trends, shocks and shifts in the data. The predominant point process model for endo-exo analysis in the field of quantitative finance is the Hawkes process. A comparison of this field with the relatively mature fields of econometrics and time series identifies the need to more rigorously control for trends and shocks. Doing so allows us to test the hypothesis that the market is "critical" -- analogous to a unit root test commonly done in economic time series -- and challenge earlier results. Continuing "lessons learned" from the time series field, it is argued that the Hawkes point process is analogous to integer valued AR time series. Following this analogy, we introduce the ARMA point process, which flexibly combines exo background activity (Poisson), shot-noise bursty dynamics, and self-exciting (Hawkes) endogenous activity. We illustrate a connection to ARMA time series models, as well as derive an MCEM (Monte Carlo Expectation Maximization) algorithm to enable MLE of this process, and assess consistency by simulation study. Remaining challenges in estimation and model selection as well as possible solutions are discussed.

[1] Wheatley, S., Wehrli, A., and Sornette, D. "The endo-exo problem in high frequency financial price fluctuations and rejecting criticality". To appear in Quantitative Finance (2018). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3239443

[2] Wheatley, S., Schatz, M., and Sornette, D. "The ARMA Point Process and its Estimation." arXiv preprint arXiv:1806.09948 (2018).

Prof. Isham Valerie, Statistical Science, University College London, UK (15:00-16:00)

Stochastic Epidemic Models: Approximations, structured populations and networks

Abstract: Epidemic models are developed as a means of gaining understanding about the dynamics of the spread of infection (human and animal pathogens, computer viruses etc.) and of rumours and other information. This understanding can then inform control measures to limit, or in some cases enhance, spread. Towards this goal, I will start from some simple stochastic transmission models, and describe some Gaussian approximations and their use for inference, illustrating this with data from a norovirus outbreak as well as from simulations. I will then discuss ways of incorporating population structure via metapopulations and networks, and the effects of network structure on epidemic spread. Finally I will briefly consider the extension to explicitly spatial mobile networks, as for example when computer viruses spread via short-range wireless or bluetooth connections.

Philipp Hermann, Institute of Applied Statistics, Johannes Kepler University Linz, Austria

Time: 14:00-15:00

LDJump: Estimating Variable Recombination Rates from Population Genetic Data

Recombination is a process during meiosis which starts with the formation of DNA double-strand breaks and results in an exchange of genetic material between homologous chromosomes. In many species, recombination is concentrated in narrow regions known as hotspots, flanked by large zones with low recombination. As recombination plays an important role in evolution, its estimation and the identification of hotspot positions is of considerable interest. In this talk we introduce LDJump, our method to estimate local population recombination rates with relevant summary statistics as explanatory variables in a regression model. More precisely, we divide the DNA sequence into small segments and estimate the recombination rate per segment via the regression model. In order to obtain change-points in recombination we apply a frequentist segmentation method. This approach controls a type I error and provides confidence bands for the estimator. Overall LDJump identifies hotspots at high accuracy under different levels of genetic diversity as well as demography and is computationally fast even for genomic regions spanning many megabases. We will present a practical application of LDJump on a region of the human chromosome 21 and compare our estimated population recombination rates with experimentally measured recombination events.

(joint work with Andreas Futschik, Irene Tiemann-Boege, and Angelika Heissl)

Professor Dr. Ingo Scholtes, Data Analytics Group, University of Zürich

Time: 15:00-16:00

Optimal Higher-Order Network Analytics for Time Series Data

Network-based data analysis techniques such as graph mining, social network analysis, link prediction and clustering are an important foundation for data science applications in computer science, computational social science, economics and bioinformatics. They help us to detect patterns in large corpora of data that capture relations between genes, brain regions, species, humans, documents, or financial institutions. While this potential of the network perspective is undisputed, advances in data sensing and collection increasingly provide us with high-dimensional, temporal, and noisy data on real systems. The complex characteristics of such data sources pose fundamental challenges for network analytics. They question the validity of network abstractions of complex systems and pose a threat for interdisciplinary applications of data analytics and machine learning.

To address these challenges, I introduce a graphical modelling framework that accounts for the complex characteristics of real-world data on complex systems. I demonstrate this approach in time series data on technical, biological, and social systems. Current methods to analyze the topology of such systems discard information on the timing and ordering of interactions, which however determines which elements of a system can influence each other via paths. To solve this issue, I introduce a modelling framework that (i) generalises standard network representations towards multi-order graphical models for causal paths, and (ii) uses statistical learning to achieve an optimal balance between explanatory power and model complexity. The framework advances the theoretical foundation of data science and sheds light on the important question when network representations of time series data are justified. It is the basis for a new generation of data analytics and machine learning techniques that account both for temporal and topological characteristics in real-world data.

Professor Paul Fearnhead, Lancaster University - 14:00-1500

Efficient Approaches to Changepoint Problems with Dependence Across Segments

Changepoint detection is an increasingly important problem across a range of applications. It is most commonly encountered when analysing time-series data, where changepoints correspond to points in time where some feature of the data, for example its mean, changes abruptly. Often there are important computational constraints when analysing such data, with the number of data sequences and their lengths meaning that only very efficient methods for detecting changepoints are practically feasible.

A natural way of estimating the number and location of changepoints is to minimise a cost that trades-off a measure of fit to the data with the number of changepoints fitted. There are now some efficient algorithms that can exactly solve the resulting optimisation problem, but they are only applicable in situations where there is no dependence of the mean of the data across segments. Using such methods can lead to a loss of statistical efficiency in situations where e.g. it is known that the change in mean must be positive.

This talk will present a new class of efficient algorithms that can exactly minimise our cost whilst imposing certain constraints on the relationship of the mean before and after a change. These algorithms have links to recursions that are seen for discrete-state hidden Markov Models, and within sequential Monte Carlo. We demonstrate the usefulness of these algorithms on problems such as detecting spikes in calcium imaging data. Our algorithm can analyse data of length 100,000 in less than a second, and has been used by the Allen Brain Institute to analyse the spike patterns of over 60,000 neurons.

(This is joint work with Toby Hocking, Sean Jewell, Guillem Rigaill and Daniela Witten.)

Dr. Sandipan Roy, Department of Mathematical Science, University of Bath (15:00-16:00)

Network Heterogeneity and Strength of Connections

Abstract: Detecting strength of connection in a network is a fundamental problem in understanding the relationship among individuals. Often it is more important to understand how strongly the two individuals are connected rather than the mere presence/absence of the edge. This paper introduces a new concept of strength of connection in a network through a nonparameteric object called “Grafield”. “Grafield” is a piece-wise constant bi-variate kernel function that compactly represents the affinity or strength of ties (or interactions) between every pair of vertices in the graph. We estimate the “Grafield” function through a spectral analysis of the Laplacian matrix followed by a hard thresholding (Gavish & Donoho, 2014) of the singular values. Our estimation methodology is valid for asymmetric directed network also. As a by product we get an efficient procedure for edge probability matrix estimation as well. We validate our proposed approach with several synthetic experiments and compare with existing algorithms for edge probability matrix estimation. We also apply our proposed approach to three real datasets- understanding the strength of connection in (a) a social messaging network, (b) a network of political parties in US senate and (c) a neural network of neurons and synapses in C. elegans, a type of worm.

Prof. Galin Jones, School of Statistics, University of Minnesota (14:00-15:00)

Bayesian Spatiotemporal Modeling Using Hierarchical Spatial Priors, with Applications to Functional Magnetic Resonance Imaging

We propose a spatiotemporal Bayesian variable selection model for detecting activation in functional magnetic resonance imaging (fMRI) settings. Following recent research in this area, we use binary indicator variables for classifying active voxels. We assume that the spatial dependence in the images can be accommodated by applying an areal model to parcels of voxels. The use of parcellation and a spatial hierarchical prior (instead of the popular Ising prior) results in a posterior distribution amenable to exploration with an efficient Markov chain Monte Carlo (MCMC) algorithm. We study the properties of our approach by applying it to simulated data and an fMRI data set.

Dr. Flavio Goncalves, Universidade Federal de Minas Gerais, Brazil (15:00-16:00).

Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes

In this talk we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.

Dr. Carlo Albert, EAWAG, Switzerland

Bayesian Inference for Stochastic Differential Equation Models through Hamiltonian Scale Separation

Bayesian parameter inference is a fundamental problem in model-based data science. Given observed data, which is believed to be a realization of some parameterized model, the aim is to find a distribution of likely parameter values that are able to explain the observed data. This so-called posterior distribution expresses the probability of a given parameter to be the "true" one, and can be used for making probabilistic predictions. For truly stochastic models this posterior distribution is typically extremely expensive to evaluate. We propose a novel approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, whose dynamics is confined by both the model and the measurements. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

Dr. Kayvan Sadeghi, University College London

Probabilistic Independence, Graphs, and Random Networks
The main purpose of this talk is to explore the relationship between the set of conditional independence statements induced by a probability distribution and the set of separations induced by graphs as studied in graphical models. I introduce the concepts of Markov property and faithfulness, and provide conditions under which a given probability distribution is Markov or faithful to a graph in a general setting. I discuss the implications of these conditions in devising structural learning algorithms, in understanding exchangeabile vectors, and in random network analysis.

 Dr. Martin Tegner, University of Oxford

A probabilistic
approach to non-parametric local volatility

 The local volatility model is a celebrated model widely used for pricing and hedging financial derivatives. While the model’s main appeal is its capability of reproducing any given surface of observed option prices—it provides a perfect fit—the essential component of the model is a latent function which can only be unambiguously determined in the limit of infinite data. To (re)construct this function, numerous calibration methods have been suggested involving steps of interpolation and extrapolation, most often of parametric form and with point-estimates as result. We seek to look at the calibration problem in a probabilistic framework with a fully nonparametric approach based on Gaussian process priors. This immediately gives a way of encoding prior believes about the local volatility function and a hypothesis model which is highly flexible whilst being prone to overfitting. Besides providing a method for calibrating a (range of) point-estimate(s), we seek to draw posterior inference on the distribution over local volatility. This to better understand the uncertainty attached with the calibration in particular, and with the model in general. Further, we seek to understand dynamical properties of local volatility by augmenting the hypothesis space with a time dimension. Ideally, this gives us means of inferring predictive distributions not only locally, but also for entire surfaces forward in time.

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Speaker: Professor Martyn Plummer, Department of Statistics, Warwick University
Title: A Bayesian Information Criterion for Singular Models

Abstract: We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher information matrices may fail to be invertible along other competing sub-models. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz’s Bayesian information criterion (BIC) and the penalty structure in BIC generally does not reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. Guided by examples such as determining the number of components of mixture models, the number of factors in latent factor models or the rank in reduced-rank regression, we propose a resolution to this paradox and give a practical extension of BIC for singular model selection problems.

2-3pm B3.02, June 15, 2018 - Sarah Heaps (Newcastle University)

Identifying the effect of public holidays on daily demand for gas

Gas distribution networks need to ensure the supply and demand for gas are balanced at all times. In practice, this is supported by a number of forecasting exercises which, if performed accurately, can substantially lower operational costs, for example through more informed preparation for severe winters. Amongst domestic and commercial customers, the demand for gas is strongly related to the weather and patterns of life and work. In regard to the latter, public holidays have a pronounced effect, which often extends into neighbouring days. In the literature, the days over which this protracted effect is felt are typically pre-specified as fixed windows around each public holiday. This approach fails to allow for any uncertainty surrounding the existence, duration and location of the protracted holiday effects. We introduce a novel model for daily gas demand which does not fix the days on which the proximity effect is felt. Our approach is based on a four-state, non-homogeneous hidden Markov model with cyclic dynamics. In this model the classification of days as public holidays is observed, but the assignment of days as “pre-holiday”, “post-holiday” or “normal” is unknown. Explanatory variables recording the number of days to the preceding and succeeding public holidays guide the evolution of the hidden states and allow smooth transitions between normal and holiday periods. To allow for temporal autocorrelation, we model the logarithm of gas demand at multiple locations, conditional on the states, using a first-order vector autoregression (VAR(1)). We take a Bayesian approach to inference and consider briefly the problem of specifying a prior distribution for the autoregressive coefficient matrix of a VAR(1) process which is constrained to lie in the stationary region. We summarise the results of an application to data from Northern Gas Networks (NGN), the regional network serving the North of England, a preliminary version of which is already being used by NGN in its annual medium-term forecasting exercise.

--

Victor Panaretos (EPFL)

What is the dimension of a stochastic process?

How can we determine whether a mean-square continuous stochastic process is, in fact, finite-dimensional, and if so, what its actual dimension is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional data analysis, which require low-dimensional representations whether by functional PCA or other methods. The difficulty is that the determination is to be made on the basis of iid replications of the process observed discretely and with measurement error contamination. This adds a ridge to the empirical covariance, obfuscating the underlying dimension. We build a matrix-completion-inspired test procedure that circumvents this issue by measuring the best possible least square fit of the empirical covariance's off-diagonal elements, optimised over covariances of given finite rank. For a fixed grid of sufficient size, we determine the statistic's asymptotic null distribution as the number of replications grows. We then use it to construct a bootstrap implementation of a stepwise testing procedure controlling the family-wise error rate corresponding to the collection of hypothesis formalising the question at hand. The procedure involves no tuning parameters or pre-smoothing, is indifferent to the homoskedasticity or lack of it in the measurement errors, and does not assume a low-noise regime. Based on joint work with Anirvan Chakraborty (EPFL).

Caitlin Buck (University of Sheffield)

A dilemma in Bayesian chronology construction

Chronology construction was one of the first applications used to show case the value of MCMC methods for Bayesian inference (Naylor and Smith, 1988; Buck et al, 1992). As a result, Bayesian chronology construction is now ubiquitous in archaeology and is becoming increasingly popular in palaeoenvironmental research. Currently available software requires users to construct the statistical models and input prior knowledge by hand, requiring considerable expertise and patience. As a result, the published chronologies for most sites are based on a single model which is assumed to be correct. Recent research has, however, led to a proposal to automate production of Bayesian chronological models from field records. The approach uses directed acyclic graphs (DAGs) to represent the site stratigraphy and, from these, construct priors for the Bayesian hierarchical models (Dye and Buck, 2015). The related software is in the developmental stage but, before it can be released, we need to decide what advice to offer users about working with the large number of potential models that the new software will construct. In this seminar I will outline how and why Bayesian methods are so widely used in chronology construction, show case the new DAG-based approach, explain the nature of the dilemma we face and hope to start a discussion about potential practical solutions.

C.E. Buck, C.D. Litton, & A.F.M. Smith (1992) Calibration of radiocarbon results pertaining to related archaeological events, Journal of Archaeological Science, Vol. 19, Iss. 5, pp 497-512.

T. S. Dye & C.E. Buck (2015) Archaeological sequence diagrams and Bayesian chronological models, Journal of Archaeological Science, Vol. 63, pp 84-93.

J. C. Naylor & A. F. M. Smith (1988) An Archaeological Inference Problem, Journal of the American Statistical Association, Vol. 83, Iss. 403, pp 588-595.

Sergio Bacallado (University of Cambridge)

Three stories on clinical trial design

The design of randomised clinical trials is one of the most classical applications of modern Statistics. The first part of this talk has to do with adaptive trial designs, which aim to minimise the harm to study participants by biasing randomisation toward arms that are performing well, or by closing experimental arms when there is early evidence of futility. We first propose a class of Bayesian uncertainty-directed trial designs, which aim to maximise information gain at the trial's conclusion, and we show in applications to various types of trial that it has superior operating characteristics when compared to simpler adaptive policies. In a second section, I will discuss the use of reinforcement learning algorithms to approximate Bayes-optimal policies given a prior for the treatment effects and a utility function combining outcomes for participants and the uncertainty of treatment effects. The last part of the talk will consider the possibility of sharing preliminary data from trials with patients and physicians who are making enrollment decisions. This practice may be in line with a trend toward patient-centred clinical research, but it presents many challenges and potential pitfalls. Through a simulation study, modelled on the landscape of Glioblastoma trials in the last 15 years, we explore how such 'permeable' designs could affect operating characteristics and the statistical validity of trial conclusions.

Joint work with Lorenzo Trippa, Steffen Ventz, and Brian Alexander

Wenyang Zhang - (University of York)

Homogeneity Pursuit in Single Index Models based Panel Data Analysis

Panel data analysis is an important topic in statistics and econometrics.
Traditionally, in panel data analysis, all individuals are assumed to share the
same unknown parameters, e.g. the same coefficients of covariates when the
linear models are used, and the differences between the individuals are
accounted for by cluster effects. This kind of modelling only makes sense if
our main interest is on the global trend, this is because it would not be able
to tell us anything about the individual attributes which are sometimes very
important. In this talk, I will present a new modelling approach, based on the
single index models embedded with homogeneity, for panel data analysis, which
builds the individual attributes in the model and is parsimonious at the same
time. I will show a data driven approach to identify the structure of
homogeneity, and estimate the unknown parameters and functions based on the
identified structure. I will show the asymptotic properties of the resulting
estimators. I will also use intensive simulation studies to show how well
the resulting estimators work when sample size is finite. Finally, I will
apply the proposed modelling idea to a public financial dataset and a UK
climate dataset, and show some interesting findings.

2nd Feb - 3pm - 4pm A1.01 - Azadeh Khaleghi (Lancaster Univeristy)

Title: Approximations of the Restless Bandit Problem

Abstract: In this talk I will discuss our recent paper on the multi-armed restless bandit problem. My focus will be on an instance of the bandit problem where the pay-off distributions are stationary $\phi$-mixing. This version of the problem provides a more realistic model for most real-world applications, but cannot be optimally solved in practice since it is known to be PSPACE-hard. The objective is to characterize a sub-class of the problem where good approximate solutions can be found using tractable approaches. I show that under some conditions on the $\phi$-mixing coefficients, a modified version of the UCB algorithm proves effective. The main challenge is that, unlike in the i.i.d. setting, the distributions of the sampled pay-offs may not have the same characteristics as those of the original bandit arms.

In particular, the $\phi$-mixing property does not necessarily carry over. This is overcome by carefully controlling the effect of a sampling policy on the pay-off distributions. Some of the proof techniques developed can be more generally used in the context of online sampling under dependence. Proposed algorithms are accompanied with corresponding regret analysis. I will ensure to make the talk accessible to non-experts.

2-3pm MA B1.01, 2 Feb, 2018 - Robin Evans - (Oxford University)

Title: Geometry and statistical model selection Abstract: TBA

Jonas Peters, Department of Mathematical Sciences, University of Copenhagen

Invariant Causal Prediction

Abstract: Why are we interested in the causal structure of a process? In classical prediction tasks as regression, for example, it seems that no causal knowledge is required. In many situations, however, we want to understand how a system reacts under interventions, e.g., in gene knock-out experiments. Here, causal models become important because they are usually considered invariant under those changes. A causal prediction uses only direct causes of the target variable as predictors; it remains valid even if we intervene on predictor variables or change the whole experimental setting. In this talk, we show how we can exploit this invariance principle to estimate causal structure from data. We apply the methodology to data sets from biology, epidemiology, and finance. The talk does not require any knowledge about causal concepts.

David Ginsbourger, Idiap Research Institute and University of Bern, http://www.ginsbourger.ch
Quantifying and reducing uncertainties on sets under Gaussian Process priors

Abstract: Gaussian Process models have been used in a number of problems where an objective function f needs to be studied based on a drastically limited number of evaluations.

Global optimization algorithms based on Gaussian Process models have been investigated for several decades, and have become quite popular notably in design of computer experiments. Also, further classes of problems involving the estimation of sets implicitly defined by f, e.g. sets of excursion above a given threshold, have inspired multiple research developments.

In this talk, we will give an overview of recent results and challenges pertaining to the estimation of sets under Gaussian Process priors, with a particular interest for to the quantification and the sequential reduction of associated uncertainties.

Based on a series of joint works primarily with Dario Azzimonti, François Bachoc, Julien Bect, Mickaël Binois, Clément Chevalier, Ilya Molchanov, Victor Picheny, Yann Richet and Emmanuel Vazquez.

3-4pm A1.01, Dec 8, 2017 - Richard Samworth

Title: High-dimensional changepoint estimation via sparse projection

Abstract: Changepoints are a very common feature of big data that arrive in the form of a data stream. We study high dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the co-ordinates. The challenge is to borrow strength across the co-ordinates to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called inspect for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimization problem derived from the cumulative sum transformation of the time series. We then apply an existing univariate changepoint estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data-generating mechanisms. Software implementing the methodology is available in the R package InspectChangepoint.

4-5pm A1.01, Dec 8, 2017 - Simon R. White, MRC Biostatistics Unit, University of Cambridge

Title: Spatio-temporal modelling and heterogeneity in neuroimaging

 Abstract: Neuroimaging allows us to gain insight into the structure and activity of the brain. Clearly, there is significant spatial structure that leads to dependencies across measurements that must be accounted for. Further, the brain as an organ is never idle, thus the local temporal behaviour is important when characterising long-term functional connectivity.

 In this talk we will discuss several approaches to modelling neuroimaging that account for these key features, namely spatio-temporal heterogeneity: a novel approach to spatial modelling as an extension to the commonly used dimension reduction technique independent component analysis (ICA) for tasked-based functional magnetic resonance imaging (fMRI); propagating subject-level heterogeneity through multi-stage analyses of dynamic functional connectivity (dFC) using resting-state fMRI (rs-fMRI), and structural development using structural MRI.

3-4pm A1.01, Nov 24, 2017 - Song Liu

Title: Trimmed Density Ratio Estimation

Abstract: Density ratio estimation has become a versatile tool in machine learning community recently. However, due to its unbounded nature, density ratio estimation is vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator which automatically identifies and trims outliers. The proposed estimator has a convex formulation, and the global optimum can be obtained via subgradient descent. We analyze the parameter estimation error of this estimator under high-dimensional settings. Experiments are conducted to verify the effectiveness of the estimator.

Speaker: Jonathan Keith (Monash University)

Title: Markov chain Monte Carlo in discrete spaces, with applications in bioinformatics and ecology

 Abstract: Efficient sampling of probability distributions over large discrete spaces is a challenging problem that arises in many contexts in bioinformatics and ecology. For example, segmentation of genomes to identify putative functional elements can be cast as a multiple change-point problem involving thousands or even millions of change-points. Another example involves reconstructing the invasion history of an introduced species by embedding a phylogenetic tree in a landscape. A third example involves inferring networks of molecular interactions in cellular systems.

 In this talk I describe a generalisation of the Gibbs sampler that allows this well known strategy for sampling probability distributions in R^n to be adapted for sampling discrete spaces. The technique has been successfully applied to each of the problems mentioned above. However, these problems remain highly computationally intensive. I will discuss a number of alternatives for efficient sampling of such spaces, and will be seeking collaborations to develop these and other new approaches.

Speaker: Davide Pigoli (King's College London)

Title: Functional data analysis of biological growth processes

 Abstract: Functional data are examples of high-dimensional data when the observed variables have a natural ordering and are generated by an underlying smooth process. These additional properties allow us to develop methods that go beyond what would be possible with classical multivariate techniques. In this talk, I will demonstrate the potential of functional data analysis for biological growth processes in two different applications. The first one is in forensic entomology, where there is the need of estimating time-dependent growth curves from experiments where larvae have been exposed to a relatively small number of constant temperature profiles. The second one is in quantitative genetics, where the growth curve is a function-valued phenotypic trait from which the continuous genetic variation needs to be estimated.

Title: Semi-supervised multiview clustering for high-dimensional data

Abstract: Although the challenges presented by high dimensional data in the context of regression are well-known and the subject of much current research, comparatively little work has been done on this in the context of clustering. In this setting, the key challenge is that often only a small subset of the covariates provides a relevant stratification of the population. Identifying relevant strata can be particularly challenging when dealing with high-dimensional datasets, in which there may be many covariates that provide no information whatsoever about population structure, or – perhaps worse – in which there may be (potentially large) covariate subsets that define irrelevant stratifications. For example, when dealing with genetic data, there may be some genetic variants that allow us to group patients in terms of disease risk, but others that would provide completely irrelevant stratifications (e.g. which would group patients together on the basis of eye or hair colour). Bayesian profile regression is a semi-supervised model-based clustering approach that makes use of a response in order to guide the clustering toward relevant stratifications. Here we consider how this approach can be extended to the "multiview" setting, in which different groups of covariates ("views") define different stratifications. We also present a heuristic alternative, some preliminary results in the context of breast cancer subtyping, and consider how the approach could also be used to integrate different 'omics datasets (assuming that each dataset provides measurements on a common set of individuals).

Korbinian Strimmer (Imperial)

An entropy approach for integrative genomics and network modeling

Multivariate regression approaches such as Seemingly Unrelated Regression (SUR) or Partial Least Squares (PLS) are commonly used in vertical data integration to jointly analyse different types of omics data measured on the same samples, such as SNP and gene expression data (eQTL) or proteomic and transcriptomic data.  However, these approaches may be difficult to apply and to interpret for computational and conceptual reasons.

Here we present a simple alternative approach to integrative genomics based on using relative entropy to characterise the overall association between two (or more) sets of omic data, and to infer the underlying corresponding association network among the individual covariates.  This approach is computationally inexpensive and can be applied to large-dimensional data sets.  A key and novel feature of our method is decomposition of the total strength between two or more groups of variables based on optimal whitening of the individual data sets.  Correspondingly, it may also be viewed as a special form of a latent-variable multivariate regression model.

We illustrate this approach by analysing metabolomic and transcriptomic data from the DILGOM study.


References:

A. Kessy, A. Lewin, and K. Strimmer. 2017. Optimal whitening and decorrelation. The American Statistician, to appear. http://dx.doi.org/10.1080/00031305.2016.1277159
T. Jendoubi and K. Strimmer. 2017. Data integration and network modeling: an entropy approach.  In prep.

"Adaptive MCMC For Everyone"

Jeffrey Rosenthal, University of Toronto

Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis
Algorithm and the Gibbs Sampler, are an extremely useful
and popular method of approximately sampling from complicated
probability distributions. Adaptive MCMC attempts to automatically
modify the algorithm while it runs, to improve its performance on
the fly. However, such adaptation often destroys the ergodicity
properties necessary for the algorithm to be valid. In this talk,
we first illustrate MCMC algorithms using simple graphical Java
applets. We then discuss adaptive MCMC, and present examples and
theorems concerning its ergodicity and efficiency. We close with
some recent ideas which make adaptive MCMC more widely applicable
in broader contexts.

Paul Birrell (MRC Biostatistics Unit, Cambridge)

Towards Computationally Efficient Epidemic Inference

In a pandemic where infection is widespread, there is no direct observation of the infection processes. Instead information comes from a variety of surveillance data schemes that are prone to noise, contamination, bias and sparse sampling. To form an accurate impression of the epidemic and to be able to make forecasts of its evolution, therefore, as many of these data streams as possible need to be assimilated into a single integrated analysis. The result of this is that the transmission model describing the infection process and the linked observation models can become computationally demanding, limiting the capacity for statistical inference in real-time.

I will discuss some of our attempts at making the inferential process more efficient, with particular focus on dynamic emulation, where the computationally expensive epidemic model is replaced by a more readily evaluated proxy, a time-evolving Gaussian process trained on a (relatively) small number of model runs at key input values, training that can be done a priori.

Marcelo Pereyra

Bayesian inference by convex optimisation: theory, methods, and algorithms.

Abstract:

Convex optimisation has become the main Bayesian computation methodology in many areas of data science such as mathematical imaging and machine learning, where high dimensionality is often addressed by using models that are log-concave and where maximum-a-posteriori (MAP) estimation can be performed efficiently by optimisation. The first part of this talk presents a new decision-theoretic derivation of MAP estimation and shows that, contrary to common belief, under log-concavity MAP estimators are proper Bayesian estimators. A main novelty is that the derivation is based on differential geometry. Following on from this, we establish universal theoretical guarantees for the estimation error involved and show estimation stability in high dimensions. Moreover, the second part of the talk describes a new general methodology for approximating Bayesian high-posterior-density regions in log-concave models. The approximations are derived by using recent concentration of measure results related to information theory, and can be computed very efficiently, even in large-scale problems, by using convex optimisation techniques. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is finally illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where they are used to explore the uncertainty about the solutions, and where convex-optimisation-empowered proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error.

Ioannis Kosmidis

Title:
Reduced-bias inference for regression models with tractable and
intractable likelihoods

Abstract:

This talk focuses on a unified theoretical and algorithmic framework
for reducing bias in the estimation of statistical models from a
practitioners point of view. We will briefly discuss how shortcomings
of classical estimators and of inferential procedures depending on
those can be overcome via reduction of bias, and provide a few
demonstrations stemming from current and past research on well-used
statistical models with tractable likelihoods, including beta
regression for bounded-domain responses, and the typically
small-sample setting of meta-analysis and meta-regression in the
presence of heterogeneity. The large impact that bias in the
estimation of the variance components can have on inference motivates
delivering higher-order corrective methods for generalised linear
mixed models. The challenges in doing that will be presented along
with resolutions stemming from current research.

Liz Ryan (KCL)

Title: Simulation-based Fully Bayesian Experimental Design

Abstract:

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of Bayesian algorithms, such as Markov chain Monte Carlo (MCMC) algorithms. However, many of the proposed algorithms have been found to be computationally intensive for complex or nonstandard design problems, such as those which require a large number of design points to be found and/or those for which the observed data likelihood has no analytic expression. In this work, we develop novel extensions of existing algorithms which have been used for Bayesian experimental design, and also incorporate methodologies which have been used for Bayesian inference into the design framework, so that solutions to more complex design problems can be found.

Yi Yu (University of Bristol)

Title: Estimating whole brain dynamics using spectral clustering

Abstract: The estimation of time-varying networks for functional Magnetic Resonance Imaging (fMRI) data sets is of increasing importance and interest. In this work, we formulate the problem in a high-dimensional time series framework and introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. NCPD is applied to various simulated data and a resting-state fMRI data set. This new methodology also allows us to identify common functional states within and across subjects. Finally, NCPD promises to offer a deep insight into the large-scale characterisations and dynamics of the brain. This is joint work with Ivor Cribben (Alberta School of Business).

Satish Iyengar - Big Data Challenges in Psychiatry

 Current psychiatric diagnoses are based primarily on self-reported experiences. Unfortu- nately, treatments for the diagnoses are not effective for all patients. One hypothesized reason is that “artificial grouping of heterogeneous syndromes with different pathophysio- logical mechanisms into one disorder.” To address this problem, the US National Institute of Mental Health instituted the Research Domain Criteria framework in 2009. This re- search framework calls for integrating data from many levels of information: genes, cells, molecules, circuits, physiology, behavior, and self-report. Clustering comes to the forefront as a key tool in this big-data effort. In this talk, we present a case study of the use of mix- ture models to cluster older adults based on measures of sleep from three domains: diary, actigraphy, and polysomnography. Challenges in this effort include the use of mixtures of asymmetric (skewed) distributions, a large number of potential clustering variables, and seeking clinically meaningful solutions. We present novel variable selection algorithms, study them by simulation, and demonstrate our methods on the sleep data. This work is joint with Dr. Meredith Wallace.

Mingli Chen

Peter Orbanz

Daniel Rudolf - Perturbation theory for Markov chains

Gonzalo Garcia Donato (Universidad Castilla La Mancha)

Criteria for Bayesian model choice

In model choice (or model selection) several statistical models are postulated as legitimate explanations for a response variable and this uncertainty is to be propagated in the inferential process. The type of questions one is aimed to answer is assorted ranging from e.g. identifying the `true’ model to produce more reliable estimates that takes into account this extra source of variability. Particular important problems of model choice are hypothesis testing, model averaging and variable selection. The Bayesian paradigm provides a conceptually simple and unified solution to the model selection problem: the posterior probabilities of the competing models. This is also named the posterior distribution over the model space and is a simple function of Bayes factors. Answering any question of interest just reduces to summarizing properly this posterior distribution.

Unfortunately, the posterior distribution may depend dramatically on the prior inputs and unlike estimation problems (where model is fixed) such sensitivity does not vanish with large sample sizes. Additionally, it is well known that standard solutions like improper or vague priors cannot be used in general as they result in arbitrary Bayes factors. Bayarri et al (2012) propose tackling these difficulties basing the assignment of prior distributions in objective contexts on a number of sensible statistical. This approach takes a step beyond a way of analyzing the problem that Jeffreys inaugurated fifty years ago.

In this talk the criteria will be presented with emphasis on those aspects who serve to characterize features of the priors that, until today, have been popularly used without a clear justification.

Originally the criteria were accompanied with an application to variable selection in regression models and here we will see how they can be useful to tackle other important scenarios like high dimensional settings or survival problems.

Claire Gormley (University College Dublin)

Clustering High Dimensional Mixed Data: Joint Analysis of Phenotypic and Genotypic Data

The LIPGENE-SU.VI.MAX study, like many others, recorded high dimensional continuous phenotypic data and categorical genotypic data. Interest lies in clustering the study participant into homogeneous groups or sub-phenotypes, by jointly considering their phenotypic and genotypic data, and in determining which variables are discriminatory.

A novel latent variable model which elegantly accommodates high dimensional, mixed data is developed to cluster participants using a Bayesian finite mixture model. A computationally efficient variable selection algorithm is incorporated, estimation is via a Gibbs sampling algorithm and an approximate BIC-MCMC criterion is developed to select the optimal model.

Two clusters or sub-phenotypes (‘healthy’ and ‘at risk’) are uncovered. A small subset of variables is deemed discriminatory which notably includes phenotypic and genotypic variables, highlighting the need to jointly consider both factors. Further, seven years after the data were collected, participants underwent further analysis to diagnose presence or absence of the metabolic syndrome (MetS). The two uncovered sub-phenotypes strongly correspond to the seven year follow up disease classification, highlighting the role of phenotypic and genotypic factors in the MetS, and emphasising the potential utility of the clustering approach in early screening. Additionally, the ability of the proposed approach to define the uncertainty in sub-phenotype membership at the participant level is synonymous with the concepts of precision medicine and nutrition.

Degui Li (University of York)

Panel Data Models with Interactive Fixed Effects and Multiple Structural Breaks

In this paper we consider estimation of common structural breaks in panel data models with interactive fixed effects which are unobservable. We introduce a penalized principal component (PPC) estimation procedure with an adaptive group fused LASSO to detect the multiple structural breaks in the models. Under some mild conditions, we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates. furthermore, we estimate the regression coefficients through the post-LASSO method and establish the asymptotic distrbution theory for the resulting estimators. The developed methodology and theory are applicable to the case of dynamic panel data models. The Monte Carlo simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist. We finally apply our method to study the environmental Kuznets curve for 74 countries over 40 years and detect two breaks in the data.

Jon Forster (Southampton)

Model integration for mortality estimation and forecasting

The decennial English Life Tables have been produced after every UK decennial census since 1841. They are based on graduated (smoothed) estimates of central mortality rates, or related functions. For UK mortality, over the majority of the age range, a GAM can provide a smooth function which adheres acceptably well to the crude mortality rates. At the very highest ages, the sparsity of the data mean that the uncertainty about mortality rates is much greater. A further issue is that life table estimation requires us to extrapolate the estimate of the mortality rate function to ages beyond the extremes of the observed data. Our approach integrates a GAM at lower ages with a low-dimensional parametric model at higher ages. Uncertainty about the threshold age ,at which the transition to the simpler model occurs, is integrated into the analysis.

This base structure can then be extended into a model for the evolution of mortality rates over time, allowing the forecasting of mortality rates, a key input into demographic projections necessary for planning.

Michael Newton (University of Wisconsin-Madison)

Ranking and selection revisited

In large-scale inference the precision with which individual parameters are estimated may vary greatly among parameters, thus complicating the task to rank order parameters. I present a framework for evaluating different ranking/selection schemes as well as an empirical Bayesian methodology showing theoretical and empirical advantages over available approaches. Examples from genomics and sports will help to illustrate the issues.

Mikhail Malyutov (Northeastern University)

Context-free and Grammer-free Statistical Testing Identity of Styles

Our theory justifies our thorough statistical modification CCC of D.Khmelev's conditional compression based classification idea of 2001 and the 7 years of intensive applied statistical implementation of CCC for authorship attribution of literary works.

Homogeneity testing based on SCOT training with applications to the financial modeling and Statistical Quality Control are also in progress. Both approaches are desrcibed in a Springer monograph which appears shortly. Stochastic Context Tree (abbreviated as SCOT) is m-Markov Chain with every state of a spring independent of the symbols in its more remote past than the context of length determined by the preceding symbols of this state.

In all of our applications we uncover a complex sparse structure of memory in SCOT models that allows excellent discrimination power. In additiion, a straightforward estimation of the stationary distributio of SCOT gives insight into contexts crucial for discrimination between, say, different regimes of financial data or between styles of different authors of literary tests.

Petros Dellaporta (UCL)

Scalable inference for a full multivariate stochastic volatility model

Abstract: We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of assets is prohibitively large, we propose a factor multivariate stochastic volatility model in which the variances and correlations of the factors evolve stochastically over time. Inference is achieved via a carefully designed feasible andscalable Markov chain Monte Carlo algorithm that combines two computationally important ingredients: it utilizes invariant to the prior Metropolis proposal densities for simultaneously updating all latent paths and has quadratic, rather than cubic, computational complexity when evaluating the multivariate normal densities required. We apply our modelling and computational methodology to 571 stock daily returns of Euro STOXX index for data over a period of 10 years.

Alan Gelfand (Duke, Dept of Statistical Science)

Title: Space and circular time log Gaussian Cox processes with application to crime event data

Abstract: We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Poisson process or with a more general Cox process, we need to specify a space-time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. In fact, we view time as circular, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. In addition, crimes are classified by crime type.

Furthermore, each crime event is marked by day of the year which we convert to day of the week. We present models to accommodate such data. Then, we extend the modeling to include the marks. Our specifications naturally take the form of hierarchical models which we t within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare separable vs. nonseparable covariance specifications. 

Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012. Again, we have location, hour, day of the year, and crime type for each event. We investigate a rich range

of models to enhance our understanding of the set of incidences.

Theresa Smith (CHICAS, Lancaster Medical School)

Modelling geo-located health data using spatio-temporal log-Gaussian Cox processes

Abstract: Health data with high spatial and temporal resolution are becoming more common, but there are several practical and computational challenges to using such data to study the relationships between disease risk and possible predictors. These difficulties include lack of measurements on individual-level covariates/exposures, integrating data measured on difference spatial and temporal units, and computational complexity.

In this talk, I outline strategies for jointly estimating systematic (i.e., parametric) trends in disease risk and assessing residual risk with spatio-temporal log-Gaussian Cox processes (LGCPs). In particular, I will present a Bayesian methods and MCMC tools for using spatio-temporal LGCPs to investigate the roles of environmental and socio-economic risk-factors in the incidence of Campylobacter in England.

Ewan Cameron (Oxford, Dept of Zoology)

Progress and (Statistical) Challenges in Malariology

Abstract: In this talk I will describe some key statistical challenges faced by researchers aiming to quantify the burden of disease arising from Plasmodium falciparum malaria at the population level. These include covariate selection in the 'big data' setting, handling spatially-correlated residuals at scale, calibration of individual simulation models of disease transmission, and the embedding of continuous-time, discrete-state Markov Chain solutions within hierarchical Bayesian models. In each case I will describe the pragmatic solutions we've implemented to-date within the Malaria Atlas Project, and highlight more sophisticated solutions we'd like to have in the near-future if the right statistical methodology and computational tools can be identified and/or developed to this end.

References:

http://www.nature.com/nature/journal/v526/n7572/abs/nature15535.html

http://www.nature.com/ncomms/2015/150907/ncomms9170/full/ncomms9170.html

http://www.ncbi.nlm.nih.gov/pubmed/25890035

http://link.springer.com/article/10.1186/s12936-015-0984-9

Li Su with Michael J. Daniels (MRC Biostatistics Unit)
Bayesian modeling of the covariance structure for irregular longitudinal data using the partial autocorrelation function
Abstract: In long-term follow-up studies, irregular longitudinal data are observed when individuals are assessed repeatedly over time but at uncommon and irregularly spaced time points. Modeling the covariance structure for this type of data is challenging, as it requires specification of a covariance function that is positive definite. Moreover, in certain settings, careful modeling of the covariance structure for irregular longitudinal data can be crucial in order to ensure no bias arises in the mean structure. Two common settings where this occurs are studies with ‘outcome-dependent follow-up’ and studies with ‘ignorable missing data’. ‘Outcome-dependent follow-up’ occurs when individuals with a history of poor health outcomes had more follow-up measurements, and the intervals between the repeated measurements were shorter. When the follow-up time process only depends on previous outcomes, likelihood-based methods can still provide consistent estimates of the regression parameters, given that both the mean and covariance structures of the irregular longitudinal data are correctly specified and no model for the follow-up time process is required. For ‘ignorable missing data’, the missing data mechanism does not need to be specified, but valid likelihood-based inference requires correct specification of the covariance structure. In both cases, flexible modeling approaches for the covariance structure are essential. In this work*, we develop a flexible approach to modeling the covariance structure for irregular continuous longitudinal data using the partial autocorrelation function and the variance function. In particular, we propose semiparametric non-stationary partial autocorrelation function models, which do not suffer from complex positive definiteness restrictions like the autocorrelation function. We describe a Bayesian approach, discuss computational issues, and apply the proposed methods to CD4 count data from a pediatric AIDS clinical trial.
*Details can be found in the paper published in Statistics in Medicine 2015, 34, 2004–2018.

Martin Lindquist (John Hopkins University, Dept of Biostatistics)

New Approaches towards High-dimensional Mediation

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the path between a randomized treatment and an outcome variable. The influence of the intermediate variable (mediator) on the outcome is often determined using structural equation models (SEMs). While there has been significant research on the topic in recent years, little is known about mediation analysis when the mediator is high dimensional. Here we discuss two approaches towards addressing this problem. The first is an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous function rather than a single scalar measure. The second finds the linear combination of a high-dimensional vector of potential mediators that maximizes the likelihood of the SEM. Both methods are applied to data from a functional magnetic resonance imaging (fMRI) study of thermal pain that sought to determine whether brain activation mediated the effect of applied temperature on self-reported pain.

Ismael Castillo (Université Paris 6, Laboratoire de Probabilités et Modèles Aléatoires)
On some properties of Polya trees posterior distributions

In Bayesian nonparametrics, Polya tree distributions form a popular and flexible class of priors on distributions or density functions. In the problem of density estimation, for certain choices of parameters, Polya trees have been shown to produce asymptotically consistent posterior distributions in a Hellinger sense. In this talk, after reviewing some general properties of Polya trees, I will show that the previous consistency result can be made much more precise in two directions: 1) rates of convergence can be derived 2) it is possible to characterise the limiting shape of the posterior distribution in a functional sense. We will discuss a few applications to Donsker-type results on the cumulative distribution function and to the study of some functionals of the density.
 

Patrick Wolfe (UCL, Dept of Statistical Science)
Network Analysis and Nonparametric Statistics

Networks are ubiquitous in today's world. Any time we make observations about people, places, or things and the interactions between them, we have a network. Yet a quantitative understanding of real-world networks is in its infancy, and must be based on strong theoretical and methodological foundations. The goal of this talk is to provide some insight into these foundations from the perspective of nonparametric statistics, in particular how trade-offs between model complexity and parsimony can be balanced to yield practical algorithms with provable properties.

Hernando Ombao (UC Irvine, Dept of Statistics)
Problems in Non-Stationary Multivariate Time Series With Applications in Brain Signals

We present new tools for analyzing complex multichannel signals using spectral methods. The key challenges are the high dimensionality of brain signals, massive size and the complex nature of the underlying physiological process – in particular, non-stationarity. In this talk, I will highlight some of the current projects. The first is a tool that identifies changes in the structure of a multivariate time series. This is motivated by problems in characterizing changes in brain signals during an epileptic seizure where a localized population of neurons

exhibits abnormal firing behavior which then spreads to other subpopulations of neurons. This abnormal firing behavior is captured by increases in signal amplitudes (which can be easily spotted by visual inspection) and changes in the decomposition of the waveforms and in the strength of dependence between different regions (which are more subtle). The proposed frequency-specific change-point detection method (FreSpeD) uses a cumulative sum test statistic within a binary segmentation algorithm. Theoretical optimal properties of the FreSpeD method will be developed. We demonstrate that, when applied to an epileptic seizure EEG data, FreSpeD identifies the correct brain region as the focal point of seizure, the time of seizure onset and the very subtle changes in cross-coherence immediately preceding seizure onset.

The goal of the second project to track changes in spatial boundaries (or more generally spatial sets or clusters) as the seizure process unfolds. A pair of channels (or a pair of sets of channels) are merged into one cluster if they exhibit synchronicity as measured by, for example, similarities in their spectra or by the strength of their coherence. We will highlight some open problems including developing a model for the evolutionary clustering of non-stationary time series.

The first project is in collaboration with Anna Louise Schröder (London School of Economics); the second is with Carolina Euan (CIMAT, Mexico), Joaquin Ortega (CIMAT, Mexico) and Ying Sun (KAUST, Saudi Arabia).

Dan Roy (University of Toronto)
Nonstandard complete class theorems

For finite parameter spaces under finite loss, there is a close link between optimal frequentist decision procedures and Bayesian procedures:

every Bayesian procedure derived from a prior with full support is admissible, and every admissible procedure is Bayes. This relationship breaks down as we move beyond finite parameter spaces. There is a long line of work relating admissible procedures to Bayesian ones in more general settings. Under some regularity conditions, admissible procedures can be shown to be the limit of Bayesian procedures. Under additional regularity, they are generalized Bayesian, i.e., they minimize the average loss with respect to an improper prior. In both these cases, one must venture beyond the strict confines of Bayesian analysis.

Using methods from mathematical logic and nonstandard analysis, we introduce the notion of a hyperfinite statistical decision problem defined on a hyperfinite probability space and study the class of nonstandard Bayesian decision procedures---namely, those whose average risk with respect to some prior is within an infinitesimal of the optimal Bayes risk. We show that if there is a suitable hyperfinite approximation to a standard statistical decision problem, then every admissible decision procedure is nonstandard Bayes, and so the nonstandard Bayesian procedures form a complete class. We give sufficient regularity conditions on standard statistical decision problems admitting hyperfinite approximations. Joint work with Haosui (Kevin) Duanmu.

Thomas Hamelryck (Bioinformatics Center, University of Copenhagen)

Inference of protein structure and ensembles using Bayesian statistics and probability kinematics

The so-called protein folding problem is the loose designation for an amalgam of closely related, unsolved problems that include protein structure prediction, protein design and the simulation of the protein folding process. We adopt a unique Bayesian approach to modelling bio-molecular structure, based on graphical models, directional statistics and probability kinematics. Notably, we developed a generative probabilistic model of protein structure in full atomic detail. I will give an overview of how rigorous probabilistic models of something as complicated as a protein's atomic structure can be formulated, focusing on the use of graphical models and directional statistics to model angular degrees of freedom. I will also discuss the reference ratio method, which is needed to "glue" several probabilistic models of protein structure together in a consistent way. The reference ratio method is based on "probability kinematics", a little known method to perform Bayesian inference proposed by the philosopher Richard C. Jeffrey at the end of the fifties. Probability kinematics might find widespread application in statistics and machine learning as a way to formulate complex, high dimensional probabilistic models for multi-scale problems by combining several simpler models.

Anjali Mazumder (University of Warwick)

Probabilistic Graphical Models for planning and reasoning of scientific evidence in the courts

The use of probabilistic graphical models (PGMs) has gained prominence in the forensic science and legal literature when evaluating evidence under uncertainty. The graph-theoretic and modular nature of the PGMs provide a flexible and graphical representation of the inference problem, and propagation algorithms facilitate the calculation of laborious marginal and conditional probabilities of interest. In giving expert testimony regarding, for example, the source of a DNA sample, forensic scientists under much scrutiny, are often asked to justify their decision-making-process. Using information-theoretic concepts and a decision-theoretic framework, we define a value of evidence criterion as a general measure of informativeness for a forensic query and collection of evidence to determine which and how much evidence contributes to the reduction of uncertainty. In this talk, we demonstrate how this approach can be used for a variety of planning problems and the utility of PGMs for scientific and legal reasoning.

Daniel Simpson (University of Warwick)

Penalising model component complexity: A principled practical approach to constructing priors

Setting prior distributions on model parameters is the act of characterising the nature of our uncertainty and has proven a critical issue in applied Bayesian statistics. Although the prior distribution should ideally encode the users’ uncertainty about the parameters, this level of knowledge transfer seems to be unattainable in practice and applied statisticians are forced to search for a “default” prior.

Despite the development of objective priors, which are only available explicitly for a small number of highly restricted model classes, the applied statistician has few practical guidelines to follow when choosing the priors. An easy way out of this dilemma is to re-use prior choices of others, with an appropriate reference.

In this talk, I will introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user- defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions.

Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations, like random effect models, spline smoothing, disease mapping, Cox proportional hazard models with time-varying frailty, spatial Gaussian fields and multivariate probit models. Further, we show how to control the overall variance arising from many model components in hierarchical models.

This joint work with Håvard Rue, Thiago G. Martins, Andrea Riebler, Geir-Arne Fuglstad (NTNU) and Sigrunn H. Sørbye (Univ. of Tromsø).

Sara van de Geer (ETH Zurich)

Norm-regularized Empirical Risk Minimization

Sara van de Geer Abstract

Zoltán Szabó, (UCL)

Regression on Probability Measures: A Simple and Consistent Algorithm

We address the distribution regression problem: we regress from probability measures to Hilbert-space valued outputs, where only samples are available from the input distributions. Many important statistical and machine learning problems can be phrased within this framework including point estimation tasks without analytical solution, or multi-instance learning. However, due to the two-stage sampled nature of the problem, the theoretical analysis becomes quite challenging: to the best of our knowledge the only existing method with performance guarantees requires density estimation (which often performs poorly in practise) and the distributions to be defined on a compact Euclidean domain. We present a simple, analytically tractable alternative to solve the distribution regression problem: we embed the distributions to a reproducing kernel Hilbert space and perform ridge regression from the embedded distributions to the outputs. We prove that this scheme is consistent under mild conditions (for distributions on separable topological domains endowed with kernels), and construct explicit finite sample bounds on the excess risk as a function of the sample numbers and the problem difficulty, which hold with high probability. Specifically, we establish the consistency of set kernels in regression, which was a 15-year-old-open question, and also present new kernels on embedded distributions. The practical efficiency of the studied technique is illustrated in supervised entropy learning and aerosol prediction using multispectral satellite images. [Joint work with Bharath Sriperumbudur, Barnabas Poczos and Arthur Gretton.]

Clifford Lam, (LSE)

Nonparametric Eigenvalue-Regularized Precision or COvariance Matrix Estimator for Low and High Frequency Data Analysis

We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size. With respect to the inverse Stein’s loss function, the inverse of our estimator is asymptotically the optimal precision matrix estimator. Asymptotic efficiency loss is defined through comparison with an ideal estimator, which assumed the knowledge of the true covariance matrix. We show that the asymptotic efficiency loss of NERCOME is almost surely 0 with a suitable split location of the data. We also show that all the aforementioned optimality holds for data with a factor structure. Our method avoids the need to first estimate any unknowns from a factor model, and directly gives the covariance or precision matrix estimator. Extension to estimating the integrated volatility matrix for high frequency data is presented as well. Real data analysis and simulation experiments on portfolio allocation are presented for both low and high frequency data.

Carlos Carvalho, (The University of Texas)

Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective
Selecting a subset of variables for linear models remains an active area of research. This article reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

Andrea Riebler, (Norwegian University of Science and Technology)
Projecting cancer incidence and mortality: Bayesian age-period-cohort models ready for routine use
Projections of age-specific cancer data are of strong interest due to demographical changes, but also advances in medical diagnosis and treatment. Although Bayesian age-period-cohort (APC) models have been shown to be beneficial compared to simpler statistical models in this context, they are not yet used in routine practice. Reasons might be two-fold. First, Bayesian APC models have been criticised for producing too wide credible intervals. Second, there might be a lack of sound and at the same time easy-to-use software. Here, we address both concerns by introducing efficient MCMC-free software and showing that probabilistic forecasts obtained by the Bayesian APC model are well calibrated. We use hitherto annual lung cancer data for females in five different countries and omit the observations from the last 10 years. Consequently, we compare the yearly predictions with the actual observed data based on the absolute error and the continuous ranked probability score. Further, we assess calibration of one-step-ahead predictive distributions.

Marina Knight (York)

Hurst exponent estimation for long-memory processes using wavelet lifting
Reliable estimation of long-range dependence parameters, such as the Hurst exponent, is a well-studied problem in the statistical literature. However, many time series observed in practice present missingness or are naturally irregularly sampled. In these settings, the current literature is sparse, with most approaches requiring heavy modifications in order to deal with the time irregularity. In this talk we present a technique for estimating the Hurst exponent of time series with long memory. The method is based on a flexible wavelet transform built by means of the lifting scheme, and is naturally suitable for series exhibiting time domain irregularity. We shall demonstrate the performance of this new method and illustrate the technique through time series applications in climatology.

Gareth Peters (UCL)
Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models
In this talk we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

Leonard Held (University of Zurich)
Adaptive prior weighting in generalized linear models
The prior distribution is a key ingredient in Bayesian inference. Prior information in generalized linear models may come from different sources and may or may not be in conflict with the observed data. Various methods have been proposed to quantify a potential prior-data conflict, such as Box's $p$-value. However, the literature is sparse on methodology what to do if the prior is not compatible with the observed data. To this end, we review and extend methods to adaptively weight the prior distribution. We relate empirical Bayes estimates of prior weight to Box's p-value and propose alternative fully Bayesian approaches. Prior weighting can be done for the joint prior distribution of the regression coefficients or - under prior independence - separately for each regression coefficient or for pre-specified blocks of regression coefficients. We outline how the proposed methodology can be implemented using integrated nested Laplace approximations (INLA) and illustrate the applicability with a logistic and a log-linear Poisson multiple regression model. This is joint work with Rafael Sauter.

Rebecca Killick (Lancaster)
Forecasting locally stationary time series
Within many fields forecasting is an important statistical tool. Traditional statistical techniques often assume stationarity of the past in order to produce accurate forecasts. For data arising from the energy sector and others, this stationarity assumption is often violated but forecasts still need to be produced. This talk will highlight the potential issues when moving from forecasting stationary to nonstationary data and propose a new estimator, the local partial autocorrelation function, which will aid us in forecasting locally stationary data. We introduce the lpacf alongside associated theory and examples demonstrating its use as a modelling tool. Following this we illustrate the new estimator embedded within a forecasting method and show improved forecasting performance using this new technique.

Peter Green (Bristol)
Inference on decomposable graphs: priors and sampling
The structure in a multivariate distribution is largely captured by the conditional independence relationships that hold among the variables, often represented graphically, and inferring these from data is an important step in understanding a complex stochastic system. We would like to make simultaneous inference about the conditional independence graph and parameters of the model; this is known as joint structural and quantitative learning in the machine learning literature. The Bayesian paradigm allows a principled approach to this simultaneous inference task. There are tremendous computational and interpretational advantages in assuming the conditional independence graph is decomposable, and not too many disadvantages. I will present a new structural Markov property for decomposable graphs, show its consequences for prior modelling, and discuss a new MCMC algorithm for sampling graphs that enables Bayesian structural and quantitative learning on a much bigger scale than previously possible. This is joint work with Alun Thomas (Utah).

Luis Nieto Barajas (ITAM - Instituto Tecnologico Autonomo de Mexico)
A Bayesian nonparametric approach for time series clustering
In this work we propose a model-based clustering method for time series. The model uses an almost surely discrete Bayesian nonparametric prior to induce clustering of the series. Specifically we propose a general Poisson-Dirichlet process mixture model, which includes the Dirichlet process mixture model as particular case. The model accounts for typical features present in a time series like trends, seasonal and temporal components. All or only part of these features can be used for clustering according to the user. Posterior inference is obtained via an easy to implement Markov chain Monte Carlo (MCMC) scheme. The best cluster is chosen according to a heterogeneity measure as well as the model selection criteria LPML (logarithm of the pseudo marginal likelihood). We illustrate our approach with a dataset of time series of shares prices in the Mexican stock exchange.

David Draper (University of California, Santa Cruz, USA, and Ebay Research Labs, San Jose, California, USA)
Why the bootstrap works; and when and why log scores are a good way to compare Bayesian models
In this talk I'll describe recent work on two unrelated topics:
(a) How the frequentist bootstrap may be understood as an approximate Bayesian non-parametric method, which explains why the bootstrap works and when it doesn't, and
(b) Why log scores are a good way to compare Bayesian models, and when they're better than Bayes factors at doing so.

David van Dyk (Imperial)
Statistical Learning Challenges in Astronomy and Solar Physics
In recent years, technological advances have dramatically increased the quality and quantity of data available to astronomers. Newly launched or soon-to-be launched space-based telescopes are tailored to data-collection challenges associated with specific scientific goals. These instruments provide massive new surveys resulting in new catalogs containing terabytes of data, high resolution spectrography and imaging across the electromagnetic spectrum, and incredibly detailed movies of dynamic and explosive processes in the solar atmosphere. The spectrum of new instruments is helping scientists make impressive strides in our understanding of the physical universe, but at the same time generating massive data-analytic and data-mining challenges for scientists who study the resulting data. In this talk I will introduce and discuss the statistical learning challenges inherent in data streams that are both massive and complex.

Daniel Williamson (Exeter)
Earth system models and probabilistic Bayesian calibration: a screw meets a hammer?
The design and analysis of computer experiments, now called “Uncertainty Quantification” or “UQ” has been an active area of statistical research for 25 years. One of the most high profile methodologies, that of calibrating a complex computer code using the Bayesian solution to the inverse problem as described by Kennedy and O’Hagan’s seminal paper in 2001, has become something of a default approach to tackling applications in UQ and has over 1200 citations. However, is this always wise? Though the method is well tested and arguably appropriate for many types of model, particularly those for which large amounts of data are readily available and in which the limitations of the underlying mathematical expressions and solvers are well understood, many models, such as those found in climate simulation, go far beyond those successfully studied in terms of non-linearity, run time, output size and complexity of the underlying mathematics. Have we really solved the calibration problem? To what extent is our “off the shelf approach” appropriate for the problems faced in fields such as Earth system modelling? In this talk we will discuss some of the known limitations of the Bayesian calibration framework (and some perhaps unknown) and we explore the extent to which the conditions in which calibration is known to fail are met in climate model problems. We will then present and argue for an alternative approach to the problem and apply it an ocean GCM known as NEMO.

Michael Eichler (Maastricht)
Causal Inference from Multivariate Time Series: Principles and Problems

In time series analysis, inference about cause-effect relationships among multiple time series is commonly based on the concept of Granger causality, which exploits temporal structure to achieve causal ordering of dependent variables. One major and well known problem in the application of Granger causality for the identification of causal relationships is the possible presence of latent variables that affect the measured components and thus lead to so-called spurious causalities. We present a new graphical approach for describing and analysing Granger-causal relationships in multivariate time series that are possibly affected by latent variables. It is based on mixed graphs in which directed edges represent direct influences among the variables while dashed edges---directed or undirected---indicate associations that are induced by latent variables. We show how such representations can be used for inductive causal learning from time series and discuss the underlying assumptions and their implications for causal learning. Finally we will discuss tetrad constraints in the time series context and how the can be exploited for causal inference.

Richard Huggins (Melbourne)
Semivarying Coefficient Models for Capture--recapture Data: Colony Size Estimation for the Little Penguin
To accommodate seasonal effects that change from year to year into models for the size of an open population we consider a time-varying coefficient model. We fit this model to a capture-recapture data set collected on the little penguin in south-eastern Australia over a 25 year period, using Jolly--Seber type estimators and nonparametric P-spline techniques. The time-varying coefficient model identified strong changes in the seasonal pattern across the years which we further examine using functional data analysis techniques.
(Joint work with Jakub Stoklosa of The University of New South Wales and Peter Dann from the Phillip Island Nature Parks.

Pierre Jacob
Estimation of the score vector and observed information matrix in intractable models
Ionides, King et al. (see Inference for nonlinear dynamical systems, PNAS 103) have introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to simulate the latent Markov model according its prior distribution. Their methodology bypasses the calculation of any derivative by expressing the score in the original model as an expectation under a modified model. Building upon this insightful work, we provide here a similar "derivative-free" estimator for the observed information matrix, expressed as a covariance matrix under a modified model. In principle the method is applicable for any latent variable model. We also discuss connections with Stein's method and proximal mappings.

Leonardo Bottolo
Mixture priors for subgroups classification
Technologies for the collection of genetic data, such as those based on RNA-Seq, are developing at a very fast rate. A crucial objective in these studies is gene clustering based on the similarity of their level of expression. A more important clustering task concerns samples themselves: this goes under the name of molecular profiling, and aims at identifying similarities across samples based on a few genes identified from the previous stage of the analysis.

In this talk we present a fully Bayesian hierarchical model for molecular profiling. A key ingredient of our approach is represented by the use of mixture distributions. First of all expression measurements are assumed to originate from a three-component mixture distribution, representing the underlying population classes (baseline, underexpression and overexpression) of samples relative to gene-expression. For each gene we assume a specific (random) probability of belonging to any of the three classes. Current Bayesian modelling assumes that the collection of gene-specific probabilities is exchangeable. Exchangeability assumption exhibits some drawbacks, the main one being its inability to capture heterogeneity in gene-behavior. This led us to model the gene-specific probabilities of under overexpression using a mixture of prior distributions with an unknown number of components: this represents the novelty of our approach which is meant to capture variation in gene behaviour and to identify clusters of genes in relation to their probability of under and overexpression.

The model is applied to gene expression levels from RNA-Seq analysis of left ventricular tissue derived from a cohort comprising 33 dilated cardiomyopathy patients with end-stage heart failure who underwent left ventricular assist device implant. Of these patients, 24 subsequently recovered their function whereas 9 did not. There is no obvious distinguishing features between them at the time the sample was taken. Molecular profiling is derived to predict recovery vs non-recovery patients. This is a joint work with Petros Dellaportas and Athanassios Petralias, Dept of Statistics, Athens University.

Karthik Bharath

Bayes robustness with Fisher-Rao metric.
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A Riemannian-geometric framework is proposed to assess sensitivity of Bayesian procedures to modeling
assumptions based on the nonparametric Fisher–Rao metric; assessments include local and global robustness to perturbations of the likelihood and prior, and identification of influential observations. An important feature of the approach is in the unification of the perturbation and the inference via intrinsic analysis on the space of probability densities under the same Riemannian metric which leads to geometrically calibrated influence measures. Utility of the framework in interesting applications involving generalized mixed-effects and directional data models will be demonstrated.


Tony O’Hagan

"What can we do with a model that's wrong?"

People use models in all fields of science, technology, management, etc. These can range from highly complex mathematical models based on systems of differential equations to relatively simple empirical, statistical, models. This talk is about the uncertainty in the predictions made by models. One aspect of this has come to be called Uncertainty Quantification (UQ), and is concerned with deriving the uncertainty in model outputs induced by uncertainty in the inputs. But there is another component of uncertainty that is much more important: all models are wrong. This talk is about just how badly misled we can be if we forget this fact.

Christophe Ley - Universite Livre de Bruxelles

Stein's method, Information theory, and Bayesian statistics

In this talk, I will first describe a new general approach to the celebrated Stein method for asymptotic approximations and apply it to diverse approximation problems. Then I will show how Stein’s method can be successfully used in two a priori unrelated domains, namely information theory and Bayesian statistics. In the latter case, I will evaluate the influence of the choice of the prior on the posterior distribution at given sample size n. Based on joint work with Gesine Reinert (Oxford) and Yvik Swan (Liege).

Adelchi Azzalini (University of Padova)

Clustering based on non-parametric density estimation: A proposal

Cluster analysis based on non-parametric density estimation represents an approach to the clustering problem whose roots date back several decades, but it is only in recent times that this approach could actually be developed. The talk presents one proposal within this approach which is among the few ones which have been brought up to the operational stage.

Emmanuele Giorgi (Lancaster)

Combining data from multiple spatially referenced prevalence surveys using generalized linear geostatistical models

Geostatistical methods are becoming more widely used in epidemiology to analyze spatial variation in disease prevalence. These methods are especially useful in resource-poor settings where disease registries are either non-existent or geographically incomplete, and data on prevalence must be obtained by survey sampling of the population of interest. In order to obtain good geographical coverage of the population, it is often necessary also to combine information from multiple prevalence surveys in order to estimate model parameters and for prevalence mapping.

However, simply fitting a single model to the combined data from multiple surveys is inadvisable without testing the implicit assumption that both the underlying process and its realization are common to all of the surveys. We have developed a multivariate generalized linear geostatistical model to combine data from multiple spatially referenced prevalence surveys so as to address each of two common sources of variation across surveys: variation in prevalence over time; variation in data-quality.

In the case of surveys that differ in quality, we assume that at least one of the surveys delivers unbiased gold-standard estimates of prevalence, whilst the others are potentially biased. For example, some surveys might use a random sampling design, the others opportunistic convenience samples. For parameter estimation and spatial predictions, we used Monte Carlo Maximum Likelihood methods.

We describe an application to malaria prevalence data from Chikhwawa District, Malawi. The data consist of two Malaria Indicator Surveys (MISs) and an Easy Access Group (EAG) study, conducted over the period 2010-2012. In the two MISs, the data were collected by random selection of households in an area of 50 villages within 400 square kilometers, whilst the EAG study enrolled a random selection of children attending the vaccination clinic in Chikhwawa District Hospital. The second sampling strategy is more economical, but the sampling bias inherent to such "convenience" samples needs to be taken into account.

Ben Graham (University of Warwick)

Handwriting, signatures, and convolutions

The 'signature', from the theory of differential equations driven by rough paths, provides a very efficient way of characterizing curves. From a machine learning perspective, the elements of the signature can be used as a set of features for consumption by a classification algorithm.

Using datasets of letters, digits, Indian characters and Chinese characters, we see that this improves the accuracy of online character recognition---that is the task of reading characters represented as a collection of pen strokes.

Randal Douc (TELECOM SudParis)

Identifiability conditions for partially-observed Markov chains By R. Douc, F. Roueff and T. Sim

This paper deals with a parametrized family of partially-observed bivariate Markov chains. We establish that the limit of the normalized log-likelihood is maximized when the parameter belongs to the equivalence class of the true parameter, which is a key feature for obtaining consistency the Maximum Likelihood Estimators (MLE) in well-specified models. This result is obtained in a general framework including both fully dominated or partially dominated models, and thus applies to both Hidden Markov models or Observation-Driven times series. In contrast with previous approaches, the identifiability is addressed by relying on the unicity of the invariant distribution of the Markov chain associated to the complete data, regardless its rate of convergence to the equilibrium. We use this approach to obtain a set of easy-to-check conditions which imply the consistency of the MLE of a general observation driven time series.

Rajen Shah (Cambridge)

Random Intersection Trees for finding interactions in large, sparse datasets

Many large-scale datasets are characterised by a large number (possibly tens of thousands or millions) of sparse variables. Examples range from medical insurance data to text analysis. While estimating main effects in regression problems involving such data is now a reasonably well-studied problem, finding interactions between variables remains a serious computational challenge. As brute force searches through all possible interactions are infeasible, most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that potentially informative high-order interactions may be overlooked. Here, we propose an alternative approach for classification problems with binary predictor variables, called Random Intersection Trees. It works by starting with a maximal interaction that includes all variables, and then gradually removing variables if they fail to appear in randomly chosen observations of a class of interest. We show that with this method, under some weak assumptions, interactions can be found with high probability, and that the computational complexity of our procedure is much smaller than for a brute force search.

David Leslie (Bristol)
Applied abstract stochastic approximation

Stochastic approximation was introduced as a tool to find the zeroes of a function under only noisy observations of the function value. A classical statistical example is to find the zeroes of the score function when observations can only be processed sequentially. The method has since been developed and used mainly in the control theory, machine learning and economics literature to analyse iterative learning algorithms, but I contend that it is time for statistics to re-discover the power of stochastic approximation. I will introduce the main ideas of the method, and describe an extension; the parameter of interest is an element of a function space, and we wish to analyse its stochastic evolution through time. This extension allows the analysis of online nonparametric algorithms - we present an analysis of Newton's algorithm to estimate nonparametric mixing distributions. It also allows the investigation of learning in games with a continuous strategy set, where a mixed strategy is an arbitrary distribution on an interval.

(Joint work with Steven Perkins)

Mark Fiecas (Warwick)
Modeling the Evolution of Neurophysiological Signals

In recent years, research into analyzing brain signals has dramatically increased, and these rich data sets require more advanced statistical tools in order to perform proper statistical analyses. Consider an experiment where a stimulus is presented many times, and after each stimulus presentation (trial), time series data is collected. The time series data per trial exhibit nonstationary characteristics. Moreover, across trials the time series are non-identical because their spectral properties change over the course of the experiment. In this talk, we will look at a novel approach for analyzing nonidentical nonstationary time series data. We consider two sources of nonstationarity: 1) within each trial of the experiment and 2) across the trials, so that the spectral properties of the time series data are evolving over time within a trial, and are also evolving over the course of the experiment. We extend the locally stationary time series model to account for nonidentical data. We analyze a local field potential data set to study how the spectral properties of the local field potentials obtained from the nucleus accumbens and the hippocampus of a monkey evolve over the course of a learning association experiment.

David Dunson (Duke University)

Robust and scalable Bayes via the median posterior

Bayesian methods have great promise in big data sets, but this promise has not been fully realized due to the lack of scalable computational methods. Usual MCMC and SMC algorithms bog down as the size of the data and number of parameters increase. For massive data sets, it has become routine to rely on penalized optimization approaches implemented on distributed computing systems. The most popular scalable approximation algorithms rely on variational Bayes, which lacks theoretical guarantees and badly under-estimates posterior covariance. Another problem with Bayesian inference is the lack of robustness; data contamination and corruption is particularly common in large data applications and cannot easily be dealt with using traditional methods. We propose to solve both the robustness and the scalability problem using a new alternative to exact Bayesian inference we refer to as the median posterior. Data are divided into subsets and stored on different computers prior to analysis. For each subset, we obtain a stochastic approximation to the full data posterior, and run MCMC to generate samples from this approximation. The median posterior is defined as the geometric median of the subset-specific approximations, and can be rapidly approximated. We show several strong theoretical results for the median posterior, including general theorems on concentration rates and robustness. The methods are illustrated through simple examples, including Gaussian process regression with outliers.

Eric Moulines (Télécom ParisTech)

Proximal Metropolis adjusted Langevin algorithm for sampling sparse distribution over high-dimensional spaces

This talk introduces a new Markov Chain Monte Carlo method to sampling sparse distributions or to perform Bayesian model choices in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines (i) a Metropolis adjusted Langevin step to propose local moves associated with the differentiable part of the target density with (ii) a proximal step based on the non-differentiable part of the target density which provides sparse solutions such that small components are shrunk toward zero. Several implementations of the proximal step will be investigated adapted to different sparsity priors or allowing to perform variable selections, in high-dimensional settings. The performance of these new procedures are illustrated on both simulated and real data sets. Preliminary convergence results will also be presented.

Professor Adrian Raftery (Washington)

Bayesian Reconstruction of Past Populations for Developing and Developed Countries

I will describe Bayesian population reconstruction, a new method for estimating past populations by age and sex, with fully probabilistic statements of uncertainty. It simultaneously estimates age-specific
population counts, vital rates and net migration from fragmentary data while formally accounting for measurement error. As inputs, it takes initial bias-corrected estimates of age-specific population counts, vital rates and net migration. The output is a joint posterior probability distribution which yields fully probabilistic interval estimates of past vital rates and population numbers by age and sex. It is designed for the kind of data commonly collected in demographic surveys and censuses and can be applied to countries with widely varying levels of data quality. This is joint work with Mark Wheldon, Patrick Gerland and Samuel Clark.

Darren Wilkinson (Newcastle)
Stochastic Modelling of Genetic Interaction in Budding Yeast

Saccharomyces cerevisiae (often known as budding yeast, or brewers yeast) is a single-celled micro-organism that is easy to grow and genetically manipulate. As it has a cellular organisation that has much in common with the cells of humans, it is often used as a model organism for studying genetics. High-throughput robotic genetic technologies can be used to study the fitness of many thousands of genetic mutant strains of yeast, and the resulting data can be used to identify novel genetic interactions relevant to a target area of biology. The processed data consists of tens of thousands of growth curves with a complex hierarchical structure requiring sophisticated statistical modelling of genetic independence, genetic interaction (epistasis), and variation at multiple levels of the hierarchy. Starting from simple stochastic differential equation

(SDE) modelling of individual growth curves, a Bayesian hierarchical model can be built with variable selection indicators for inferring genetic interaction. The methods will be applied to data from experiments designed to highlight genetic interactions relevant to telomere biology.

Richard Everitt (Reading)

Inexact approximations for doubly and triply intractable problems

Markov random field models are used widely in computer science, statistical physics and spatial statistics and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to an intractable likelihood function. Several methods have been developed that permit exact, or close to exact, simulation from the posterior distribution. However, estimating the marginal likelihood and Bayes' factors for these models remains challenging in general. This talk will describe new methods for estimating Bayes' factors that use simulation to circumvent the evaluation of the intractable likelihood, and compare them to approximate Bayesian computation. We will also discuss more generally the idea of "inexact approximations".

Vasileios Maroulas (Bath/Tennessee)

Filtering, drift homotopy and target tracking

Abstract:
Target tracking is a problem of paramount importance arising in Biology, Defense, Ecology and other scientific fields. We attack to this problem by employing particle filtering. Particle filtering is an importance sampling method which may fail in several occasions, e.g. in high dimensional data. In this talk, we present a novel approach for improving particle filters suited to target tracking with a nonlinear observation model. The suggested approach is based on what I
will call drift homotopy for stochastic differential equations which describe the dynamics of the moving target. Based on drift homotopy, we design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particles closer to the observations while at the same time respecting the dynamics. The talk is based on joint works with Kai Kang and Panos Stinis.

Amanda Turner (Lancaster)

Small particle limits in a regularized Laplacian random growth model
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In 1998 Hastings and Levitov proposed a one-parameter family of models for planar random growth in which clusters are represented as compositions of conformal mappings. This family includes physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth. In the simplest case of the model (corresponding to the parameter alpha=0), James Norris and I showed how the Brownian web arises in the limit resulting from small particle size and rapid aggregation. In particular this implies that beyond a certain time, all newly aggregating particles share a single common ancestor. I shall show how small changes in alpha result in the emergence of branching structures within the model so that, beyond a certain time, the number of common ancestors is a random number whose distribution can be obtained. This is based on joint work with Fredrik Johansson Viklund (Columbia) and Alan Sola (Cambridge).

Jean-Michel Marin

Consistency of the Adaptive Multiple Importance Sampling (joint work with Pierre Pudlo and Mohammed Sedki

Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of a recycling procedure. However, the consistency of the AMIS estimator remains largely open. In this work, we prove the convergence of the AMIS, at a cost of a slight modification in the learning process. Numerical experiments exhibit that this modification might even improve the original scheme.

Judith Rousseau

Asymptotic properties of Empirical Bayes procedures – in parametric and non parametric models

In this work we investigate frequentist properties of Empirical Bayes procedures. Empirical Bayes procedures are very much used in practice in more or less formalized ways as it is common practice to replace some hyperparameter in the prior by some data dependent quantity. There are typically two ways of constructing these data dependent quantities : using some king of moment estimator or some quantity whose behaviour is well understood or using a maximum marginal likelihood estimator. In this work we first give some general results on how to determine posterior concentration rates under the former setting, which we apply in particular to two types of Dirichlet process mixtures. We then shall discuss more parametric models in the context of maximum marginal likelihood estimation. We will in particular explain why some pathological behaviour can be expected in this case.

John Fox (Oxford & UCL/Royal Free Hospital)
Arguing logically about risks: strengths, limitations and a request for assistance
Abstract: The standard mathematical treatment of risk combines numerical measures of uncertainty (usually probabilistic) and loss (money and other natural estimators of utility). There are significant practical and theoretical problems with this interpretation. A particular concern is that the estimation of quantitative parameters is frequently problematic, particularly when dealing with one-off events such as political, economic or environmental disasters.
Consequently practical decision-making under risk often requires extensions to the standard treatment.
An intuitive approach to reasoning under uncertainty has recently become established in computer science and cognitive science based on argumentation theory. On this approach theories about an application domain (formalised in a non-classical first-order logic) are applied to propositional facts about specific situations, and arguments are constructed for and/or against claims about what might happen in those situations. Arguments can also attack or support other arguments. Collections of arguments can be aggregated to characterize the type or degree of risk, based on the grounds of the arguments. The grounds and form of an argument can also be used to explain the supporting evidence for competing claims and assess their relative credibility. This approach has led to a novel framework for developing versatile risk management systems and has been validated in a number of domains, including clinical medicine and toxicology (e.g. www.infermed.com; www.lhasa.com). Argumentation frameworks are also being used to support open discussion and debates about important issues (e.g. see debate on "planet under pressure" at http://debategraph.org/Stream.aspx?nid=145319&vt=bubble&dc=focus).

Despite the practical success of argumentation methods in risk management and other kinds of decision making the main theories ignore quantitative measurement of uncertainty, or they combine qualitative reasoning with quantitative uncertainty in ad hoc ways. After a brief introduction to argumentation theory I will demonstrate some medical applications and invite suggestions for ways of incorporating uncertainty probabilistically that are mathematically satisfactory.

Chenlei Leng (Warwick)

High dimensional influence measure

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure. This is joint work with Junlong Zhao, Lexin Li, and Hansheng Wang.

A copy of the paper is downloadable from http://arxiv.org/abs/1311.6636.

Selection of (ABC) summary statistics towards estimation and model choice

Abstract: The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions, which amount to the expectations of the summary statistics to asymptotically differ under both models, are then usable in ABC settings to determine which summary statistics are appropriate, via a standard and quick Monte Carlo validation. We also discuss new schemes to automatically select efficient summary statistics from a large collection of those.

(Joint work with J.-M. Marin, N. Pillai, P. Pudlo & J. Rousseau)

Statistical modelling of summary values leads to accurate Approximate Bayesian Computations

Abstract: Approximate Bayesian Computations (ABC) are considered to be noisy. We present a statistical framework for accurate ABC parameter inference that rests on well-established results from indirect inference and decision theory. This framework guarantees that ABC estimates the mode of the true posterior density exactly and that the Kullback-Leibler divergence of the ABC approximation to the true posterior density is minimal, provided that verifiable conditions are met. Our approach requires appropriate statistical modelling of the distribution of "summary values" - data points on a summary level - from which the choice of summary statistics follows implicitly. This places elementary statistical modelling at the heart of ABC analyses, which we illustrate on several examples.

Ben Francis
Stochastic Control Methods to Individualise Drug Therapy by Incorporating Pharmacokinetic, Pharmacodynamic and Adverse Event Data
There are a number of methods available to aid determination of an individualised dosage regimen for a patient. However, often these methods are non-adaptive to the patient's requirements and do not allow for changing clinical targets throughout the course of therapy.

Research has been undertaken to include process noise in the Pharmacokinetic/Pharmacodynamic (PK/PD) response prediction to better simulate the patient response to the dose by allowing values sampled from the individual PK/PD parameter distributions to vary over time.

Further work explores different formulations of a cost function by considering probabilities from a Markov model.

Using the introduced methodology, the drug dose algorithm is shown to be adaptive to patient needs for imatinib and simvastatin therapy.

However, application of the drug dose algorithm in a wide range of clinical dosing decisions is possible.

Juhyun Park (Lancaster)
Functional average derivative regression
Abstract: Single index model is studied in the framework of regression estimation involving functional data. The model extends a linear model with an unknown link function and has the advantage of having low sensitivity to dimensional effects and flexibility and easiness of interpretation. However its usage in functional regression setting is still found to be limited, partly due to its complexity of fitting the model. In this work we develop a functional adaptation of the average derivative method that allows us to construct an explicit estimator for the functional single index.
Thanks to its explicit form of the estimator, implementation is made relatively simple and straightforward. Theoretical properties of the estimator of the index are studied based on asymptotic results on nonparametric functional derivatives estimation. In particular it is shown that the nonlinear regression component of the model can be estimated at the standard univariate rate, being therefore insensitive to the infinite dimensionality of the data.

Numerical examples are used to illustrate the method and to evaluate finite sample performance.

François Caron (Oxford)
Bayesian nonparametric models for bipartite graphs

In this talk I will present a novel Bayesian nonparametric model for bipartite graphs, based on the theory of completely random measures. The model is able to handle a potentially infinite number of nodes and has appealing properties; in particular, it may exhibit a power-law behavior for some values of the parameters. I derive a posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation. Finally, the model is shown to provide a good fit to several large real-world bipartite social networks.

Davide Pigoli (Warwick)
Statistical methods for phonetic covariance operators in comparative linguistics

Comparative linguistics is concerned with the exploration of languages evolution. The traditional way of exploring relationships across languages consists of examining textual similarity. However, this neglects the phonetic characteristics of the languages. Here a novel approach is proposed to incorporate phonetic information, based on the comparison of frequency covariance structures in spoken languages. In particular, the aim is to explore the relationships among Romance languages and how they have developed from their common Latin root. The covariance operator being the statistical unit, a framework is illustrated for inference concerning the covariance operator of a functional random process. First, the problem of the definition of possible metrics for covariance operators is considered. In particular, an infinite dimensional analogue of the Procrustes reflection size and shape distance is developed. Then, distance-based inferential procedures are proposed for estimation and hypothesis testing. Finally, it is shown that the analysis of pairwise distances between phonetic covariance structures can provide insight into the relationships among Romance languages. Some languages also present features that are not completely expected from linguistics theory, indicatingnew directions for investigations.

Professor Donald Martin (North Carolina State University)

Computing probabilities for the discrete scan statistic through slack variables

The discrete scan statistic is used in many areas of applied probability and statistics to study local clumping of patterns.

Testing based on the statistic requires tail probabilities. Whereas the distribution has been studied extensively, most of the results are approximations, due to the difficulties associated with the computation. Results for exact tail probabilities for the statistic have been given for a binary sequence that is independent or first-order Markovian. We give an algorithm to obtain probabilities for the statistic over multi-state trials that are Markovian of a general order of dependence, and explore the algorithm’s usefulness.

Nicolai Meinshausen (University of Oxford)

Min-wise hashing for large-scale regression and classification.

We take a look at large-scale regression analysis in a "large p, large n" context for a linear regression or classification model.

In a high-dimensional "large p, small n" setting, we can typically only get good estimation if there exists a sparse regression vector that approximates the observations. No such assumptions are required for large-scale regression analysis where the number of observations n can (but does not have to) exceed the number of variables p. The main difficulty is that computing an OLS or ridge-type estimator is computationally infeasible for n and p in the millions and we need to find computationally efficient ways to approximate these solutions without increasing the prediction error by a large amount. Trying to find interactions amongst millions of variables seems to be an even more daunting task. We study a small variation of the b-bit minwse-hashing scheme (Li and Konig, 2011) for sparse datasets and show that the regression problem can be solved in a much lower-dimensional setting as long as the product of the number of non-zero elements in each observation and the l2-norm of a good approximation vector is small. We get finite-sample bounds on the prediction error. The min-wise hashing scheme is also shown to fit interaction models. Fitting interactions does not require an adjustment to the method used to approximate linear models, it just requires a higher-dimensional mapping.

Piotr Fryzlewicz (London School of Economics)

Wild Binary Segmentation for multiple change-point detection

We propose a new technique, called Wild Binary Segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points, unlike standard Binary Segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to significant increase in computational complexity. WBS is also easy to code. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance. In addition, we provide a new proof of consistency of Binary Segmentation with improved rates of convergence, as well as a corresponding result for WBS.

Ajay Jasra (National University of Singapore)

On the convergence of Adaptive sequential Monte Carlo Methods

In several implementations of Sequential Monte Carlo (SMC) methods, it is natural and important in terms of algorithmic efficiency, to exploit the information on the history of the particles to optimally tune their subsequent propagations. In the following talk we provide an asymptotic theory for a class of such adaptive SMC methods. Our theoretical framework developed here will cover for instance, under assumptions, the algorithms in Chopin (2002), Jasra et al (2011), Schafer & Chopin (2013). There are limited results about the theoretical underpinning of such adaptive methods: we will bridge this gap by providing a weak law of large numbers (WLLN) and a central limit theorem (CLT) for some of the algorithms. The latter seems to be the first result of its kind in the literature and provides a formal justification of algorithms that are used in many practical scenarios. This is a joint work with Alex Beskos (NUS/UCL).

Tom Palmer (Warwick Medical School)

Topics in instrumental variable estimation: structural mean models and bounds

One aim of epidemiological studies is to investigate the effect of a risk factor on a disease outcome. However, these studies are prone to unmeasured confounding and reverse causation. The use of genotypes as instrumental variables, known as Mendelian randomization studies, are one way to overcome this.

In this talk I describe some methods in instrumental variable estimation; structural mean models and nonparametric bounds for the average causal effect. Specifically, I describe how to estimate structural mean models using multiple instrumental variables in the generalized method of moments framework common in Econometrics. I describe the nonparametric bounds for the average causal effect of Balke and Pearl (JASA, 1997) which can be applied when each of the three variables; instrument, intermediate, and outcome are all binary.

I describe some methodological extensions to these bounds and their limitations.

To demonstrate the models I use a Mendelian randomization example investigating the effect of being overweight on the risk of hypertension in the Copenhagen General Population Study. I will also draw some comparisons with the application of instrumental variables to correct for noncompliance in randomized controlled trials.

Ioanna Manolopoulou (University College London)

Bayesian observation modeling in presence-only data

The prevalence of presence-only samples eg. in ecology or criminology has led to a variety of statistical approaches. Aiming to predict ecological niches, species distribution models provide probability estimates of a binary response (presence/absence) in light of a set of environmental covariates. Similarly, statistical models to predict crime use propensity indicators from observable attributes inferred from incidental data. However, the associated challenges are confounded by non-uniform observation models; even in cases where observation is driven by seemingly irrelevant factors, these may distort estimates about the distribution of occurrences as a function of covariates due to unknown correlations. We present a Bayesian non-parametric approach to addressing sampling bias by carefully incorporating an observation model in a partially identifiable framework with selectively informative priors and linking it to the underlying process. Any available information about the role of various covariates in the observation process can then naturally enter the model. For example, in cases where sampling is driven by presumed likelihood of detecting an occurrence, the observation model becomes a proxy of the presence/absence model. We illustrate our methods on an example from species distribution modeling and a corporate accounting application.

Joint work with Richard Hahn from Chicago Booth.

Dr Jon Warren (University of Warwick)

Random matrices, Stochastic Growth models and the KPZ equation.

I will base this talk on two pieces of joint work. One with Peter Windridge, the other with Neil O'Connell. Firstly I will show you how the distribution of a largest eigenvalue of certain random matrix ( in fact having a Wishart distribution) arises also in a simple stochastic growth model. In fact this growth model belongs to a large universality class, which includes mathematical models for interfaces as diverse as the edge of a burning piece of paper, or a colony of bacteria on a petri dish. The KPZ equation is a stochastic partial differential equation that also belongs to this universality class, and in the work with Neil we set out to construct an analogue, for the KPZ equation, for the second, third and so on largest eigenvalues of the random matrix.

Heather Battey (University of Bristol)

Smooth projected density estimation

In this talk I will introduce a new class of estimators for multidimensional density estimation. The estimators are attractive in that they offer both flexibility and the possibility of incorporating structural constraints, whilst possessing a succinct representation that may be stored and evaluated easily. The latter property is of paramount importance when dealing with large datasets, which are now commonplace in many application areas. We show in a simulation study that the approach is universally unintimidated across a range of data generating mechanisms and often outperforms popular nonparametric estimators (including the kernel density estimator), even when structural constraints are not utilised. Moreover, its performance is shown to be somewhat robust to the choice of tuning parameters, which is an important practical advantage of our procedure.

Kevin Korb (Monash)

An Overview of Bayesian Network Research at Monash

Recent research on and around Bayesian net (BN) technology at Monash has featured: fog forecasting (the Bureau of Meteorology); environmental management (Victorian gov); biosecurity (ACERA); finding better discretizations, using cost-based data and Bayesian scoring rules; data mining dynamic Bayesian networks; re-activating MML causal discovery of linear models. I'll discuss these and some other BN activities, briefly describe other research happening at Monash FIT, and the opportunities for collaboration.

Andrew Golightly (Newcastle University)

Auxiliary particle MCMC schemes for partially observed Markov jump processes

We consider Bayesian inference for parameters governing Markov jump processes (MJPs) using discretely observed data that may be incomplete and subject to measurement error. We use a recently proposed particle MCMC scheme which jointly updates parameters of interest and the latent process and present a vanilla implementation based on a bootstrap filter before considering improvements based around an auxiliary particle filter. In particular, we focus on a linear noise approximation to the MJP to construct a pre-weighting scheme and couple this with a bridging mechanism. Finally, we embed this approach within a 'delayed acceptance' framework to allow further computational gains. The methods are illustrated with some examples arising in systems biology.

Philip Dawid (University of Cambridge

Theory and Applications of Proper Scoring Rules

We give an overview of the theory of proper scoring rules, and some recent applications.

A proper scoring rule encourages honest assessment of personal probabilities. It can also be used to define general entropy functions, discrepancy functions, M-estimators, etc., and to extend composite likelihood methods.

We have recently characterised those proper local scoring rules that can be computed without requiring the normalising constant of the density. This property is valuable for many purposes, including Bayesian model selection with improper priors.

Catriona Queen (The Open University)

A graphical dynamic approach to forecasting flows in road traffic networks

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This talk considers how cubic splines can be used to incorporate information from these extra variables to enhance flow forecasts. The talk also introduces a new type of chain graph model for forecasting traffic flows. The models are applied to the problem of forecasting multivariate road traffic flows at the intersection of three busy motorways near Manchester, UK.

Evangelos Evangelou (University of Bath)

Spatial sampling design under cost constraints in the presence of sampling errors

A sampling design scheme for spatial models for the prediction of the underlying Gaussian random field will be presented. The optimality criterion is the maximisation of the information about the random field contained in the sample. The model discussed departs from the typical spatial model by assuming measurement error in the observations, varying from location to location, while interest lies in prediction without the error term. In this case multiple samples need to be taken from each sampling location in order to reduce the measurement error. To that end, a hybrid algorithm which combines simulated annealing nested within an exchange algorithm will be presented for obtaining the optimal sampling design. Consideration is made with regards to optimal sampling under budget constraints accounting for initialisation and sampling costs.

Joint work with Zhengyuan Zhu (Iowa State)

Dr Anastasia Papavasiliou (University of Warwick)

Statistical Inference for differential equations driven by rough paths

Differential equations driven by rough paths (RDEs for short) generalize SDEs by allowing the equation to be driven by any type of noise and not just Brownian motion. As such, they are a very flexible modelling tool for randomly evolving dynamical systems. So far, however, they have been ignored by the statistics community, in my opinion for the two followin reasons: (i) the abstract theory of rough paths is still very young and under development, which makes it very hard to penetrate; (ii) there are no statistical tools available. In this talk, I will give an introduction to the theory and I will also discuss how to approach the problem of statistical inference given a discretely observed solution to an RDE.

Bjarki Eldon (Institut für Mathematik, TU Berlin)

Single, and multiple loci, large offspring number population models

For many organisms the usual Wright-Fisher and Moran low offspring number population models are reasonable approximations. For some marine organisms (at least), this may not be the case, and one may need to consider large offspring number models, in which individuals can give rise to very many offspring, or on the order of the population size. The coalescent processes derived from the two classes of population models are very different. Examples of single, and multiple loci, population models will be discusses, and the implications large offspring number models have for inference of, for example, natural selection.

Nick Whiteley (University of Bristol)

Twisted Particle Filters

This talk reports on an investigation of alternative sampling laws for particle filtering algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. The focus is on the regime where the length of the data record tends to infinity.

Amongst a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from that of standard algorithms and yet the fluctuation properties of the estimates it provides are, in some ways, dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term "twisted" particle filters, and whose properties will be discussed.

Piotr Zwiernik (TU Eindhoven)

Group invariance for Graphical Gaussian models

Graphical models are a popular way of modeling complicated dependencies. In the Gaussian case they have a particularly simple structure. Let G be an undirected graph with n nodes. Then the graphical Gaussian model is parametrized by the set K(G) of all concentration (symmetric, positive definite) matrices with zeros corresponding to non-edges of G. In this talk I describe the maximal subgroup of the general linear group that stabilizes K(G) in the natural action on symmetric matrices. This group gives the representation of graphical Gaussian models as composite transformation families, which has important consequences for the study of this model class. In particular I show how this links to the concept of robustness of covariance matrix estimators and more classical topics like hypotheses testing. (This is joint work with Jan Draisma and Sonja Kuhnt)

Chris Sherlock (Lancaster University)

Inference for reaction networks using the Linear Noise Approximation

We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE), or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model, and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The Linear Noise Approximation (LNA) is a first order Taylor expansion of the approximating SDE about a deterministic solution. It can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how the LNA can be used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the method to the Google Flu Trends data for New Zealand, using an SEIR "community" model with separate compartments for North and South Islands.

 Robert G. Cowell (City University London)

A simple greedy algorithm for reconstructing pedigrees

I present a simple greedy-search algorithm for finding high likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but I believe that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not require age or sex information, but this information can be incorporated if desired. Prior information concerning pedigree structure is readily incorporated after the greedy-search is completed, on the high-likelihood pedigrees found.The algorithm is applied to human and non-human genetic data and in a simulation study.

Patrick Wolfe (UCL)

Modelling Network Data

Networks are fast becoming a primary object of interest in statistical data analysis, with important applications spanning the social, biological, and information sciences. A common aim across these fields is to test for and explain the presence of structure in network data. In this talk we show how characterizing the structural features of a network corresponds to estimating the parameters of various random network models, allowing us to obtain new results for likelihood-based inference and uncertainty quantification in this context. We discuss asymptotics for stochastic blockmodels with growing numbers of classes, the determination of confidence sets for network structure, and a more general point process modeling for network data taking the form of repeated interactions between senders and receivers, where we show consistency and asymptotic normality of partial-likelihood-based estimators related to the Cox proportional hazards model (arXiv:1201.5871, 1105.6245, 1011.4644, 1011.1703).

Paul Jenkins (University of Warwick)

Sequential importance sampling and resampling in population genetic inference

Since 2008, the reduction in DNA sequencing costs has far outpaced Moore's law, giving rise to a wealth of data on sequence variation in contemporary populations. The patterns of variation we see are shaped both by biological processes such as mutation, recombination, and natural selection, and by demographic processes such as population expansion, contraction, and migration. In principle the nature of these processes can be inferred from the data, and one powerful approach is to use a stochastic model like Kingman's coalescent for the random genealogical relationships relating the sampled sequences. The problem then is to compute the likelihood under this model, which can be computationally very challenging. In this talk I will describe how we can make progress on this problem by using the Monte Carlo-based approaches of sequential importance sampling and resampling. I will discuss our approach to questions including the design of a suitable proposal distribution, and when and how to resample the particle-based approximation to the posterior distribution of genealogies.

Ann Berrington (Southampton University)

Title: Gender, turning points and boomerangs: longitudinal analyses of returning home in Britain

Beatrijs Moerkerke (Ghent University, Belgium)

Estimation of controlled direct effects in the presence of exposure-induced confounding and latent variables

Estimation of the direct effect of an exposure on an outcome requires adjustment for confounders of the exposure-induced and mediator-outcome relationships. When some of these confounders are affected by the exposure, standard regression adjustment is prone to possibly severe bias. The use of inverse probability weighting has recently been suggested as a solution in the psychological literature. In this presentation, we present G-estimation as an alternative. We show that this estimation method can be easily embedded within the structural equation modeling framework and may in particular be used for estimating direct effects in the presence of latent variables. By avoiding inverse probability weighting, it accommodates the problem of unstable weights. We illustrate the approach both by simulations and by the analysis of an empirical study on the basis of which we explore the effect of age on negativity that is not mediated by mindfulness.

Pat Carter (WSU, Biology)
Evolution of Biological Shape: A Function-Valued Approach

15.00 - 16.00 Simon Tavaré (Cambridge)
Approximate Bayesian Computation for modeling DNA replication dynamics

16.30 - 17.30 Simon French (Warwick)
Aggregating expert judgement in major societal decisions

Michael Sørensen (Copenhagen)
Martingale estimating functions for stochastic differential equations with jumps

Dr Anthony Lee (Warwick)

Roberto Leon-Gonzalez, National Graduate Institute for Policy Studies, Tokyo

Endogeneity and Panel Data in Growth Regressions: A Bayesian Model Averaging Approach

In the empirical growth literature different modeling choices have led to substantially different qualitative results. Even on the basis of similar datasets, such differences can arise because of different set of instruments, exogeneity restrictions or set of controlling regressors. In this paper we develop a Bayesian Model Averaging (BMA) technique to deal with the large number of modeling choices that typically arise in the empirical growth literature. In particular, we present a general framework that not only allows for cross-section regressions with instrumental variables, but also for the commonly used dynamic panel data model with endogenous or predetermined regressors. We apply our technique to the long and inconclusive literature on the effect of international aid on GDP growth. We do not find evidence to support that international aid has an impact on GDP,
or that this impact is positive when conditioning on good macroeconomic policies. Instead we find strong evidence that macroeconomic policies, such as controlled inflation, are important
for GDP growth in developing countries.

Heather Battey (University of Bristol)

Further details to follow

Heather Battey (University of Bristol)

Graham Wood (Macquarie University and Warwick Systems Biology)

Normalization of ratio data

Quantitative mass spectrometry techniques are commonly used for comparative proteomic analysis in order to provide relative quantitation between samples. For example, in attempting to find the proteins expressed in ovarian cancer, the quantities of a given protein are assessed by mass spectrometry in separate samples of both cancerous and healthy cells. To account for the variable “loading” (the total volumes of samples) from one sample to the other, a normalization procedure is required. A common approach to normalization is to use internal standards, proteins that are assumed to display only minimal changes in abundance between the samples under comparison. A normalization procedure then allows adjustment of the data, so enabling true relative quantities to be reported.

Normalization is determined by centring the symmetrized ratio (say, cancerous over healthy) internal standards data. This presentation makes two contributions to an understanding of ratio normalization. First, the customary centring of logarithmically transformed ratios (frequently used, for example, in microarray analyses) is shown to attend not only to centring but also to minimisation of the spread of the symmetrized data. Second, the normalization problem is set in a larger context, allowing normalization to be achieved based on a symmetrization which carries the ratios to approximate normality, so increasing the power with which under or over-expressed proteins can be detected. Both simulated and real data will be used to illustrate the new method.

Stephen Connor (University of York)

State-dependent Foster-Lyapunov criteria

Foster-Lyapunov drift criteria are a useful way of proving results about the speed of convergence of Markov chains. Most of these criteria involve examining the change in expected value of some function of the chain over one time step. However, in some situations it is more convenient to look at the change in expectation over a longer time period, which perhaps varies with the current state of the chain.

This talk will review some joint work with Gersende Fort (CNRS-TELECOM ParisTech), looking at when such state-dependent drift conditions hold and (perhaps more interestingly) what can be inferred from them. (Sadly I can't promise many pictures on this occasion, but I do promise not to show any proofs!)

Yee Whye Teh (Gatsby Computational Neuroscience Unit, UCL)

A Bayesian nonparametric model for genetic variations based on fragmentation-coagulation processes

Hudson's coalescent with recombination (aka ancestral recombination
graph (ARG)) is a well accepted model of genetic variation in
populations. With growing amounts of population genetics data, demand
for probabilistic models to analyse such data is strong, and the ARG
is a very natural candidate. Unfortunately posterior inference in the
ARG is intractable, and a number of approximations and alternatives
have been proposed. A popular class of alternatives are based on
hidden Markov models (HMMs), which can be understood as approximating
the tree-structured genealogies at each point of the chromosome with a
partition of the observed haplotypes. However due to the way HMMs
parametrize partitions using latent states, they suffer from
significant label-switching issues affecting the quality of posterior
inferences.

We propose a novel Bayesian nonparametric model for genetic variations
based on Markov processes over partitions called
fragmentation-coagulation processes. In addition to some interesting
properties, our model does not suffer from the label-switching issues
of HMMs. We derive an efficient Gibbs sampler for the model and report
results on genotype imputation.

Joint work with Charles Blundell and Lloyd Elliott

Theodor Stewart (University of Cape Town)

Principles and Practice of Multicriteria Decision Analysis

The role of multicriteria decision analysis (MCDA) in the broader context of decision science will be discussed. We will review the problem structuring needs of MCDA, and caution against over-simplistic approaches. Different schools of thinking in MCDA, primarily for deterministic problems, will be introduced, to demonstrate that even such problems include many complexities and pitfalls. The practicalities will be illustrated by means of value function methods (and perhaps goal programming if time permits). We will conclude with consideration of the impact of uncertainty on MCDA and the role of scenario planning in this regard.

Shinto Eguchi (Institute of Statistical Mathematics, Japan)

Maximization of a generalized t-statistic for linear discrimination in the two group classification problem

We discuss a statistical method for the classification problem with two groups labelled 0 and 1. We envisage a situation in which the conditional distribution given label 0 is well specified by a normal distribution, but the conditional distribution given label 1 is not well modelled by any specific distribution. Typically in a case-control study the distribution in the control group can be assumed to be normal, however the distribution in the case group may depart from normality. In this situation the maximum t-statistic for linear discrimination, or equivalently Fisher's linear discriminant function, may not be optiimal. We propose a class of generalized t-statistics and study asymptotic consistency and normality. The optimal generalized t-statistic in the sense of asymptotic variance is derived in a semi-parametric manner, and its statistical performance is confirmed in several numerical experiments.

Mark Strong (University of Sheffield)

Managing Structural Uncertainty in Health Economic Decision Models

It was George Box who famously wrote ‘Essentially, all models are wrong’. Given our limited understanding of the highly complex world in which we live this statement seems entirely reasonable. Why then, in the context of health economic decision modelling, do we often act as if our models are right even if we know that they are wrong?

Imagine we have built a deterministic mathematical model to predict the costs and health effects of a new treatment, in comparison with an existing treatment. The model will be used by NICE to inform the decision as to whether to recommend the new treatment for use in the NHS.

The inputs to the model are uncertain, and we quantify the effect of this input uncertainty on the model output using Monte Carlo methods. We may even quantify the value of obtaining more information. We present our results to NICE as a fait accompli.

But, if we believe George Box then surely we should consider that our model output, our uncertainty analysis, and our estimates of the value of information are all ‘wrong’ because they are generated by a model that is ‘wrong’! The challenge is to quantify how wrong, and then determine the value of improving the model.

This seminar will explore the problem of structural uncertainty in health economic decision models, along with some suggested approaches to managing this uncertainty.

Almost all interesting problems that the brain solves involve probabilities inference; and the brain is clearly astonishingly effective at solving such problems. A substantial movement in cognitive science, neuroscience and artificial intelligence has suggested that the brain may, to some approximation, be a Bayesian. This talk considers in what sense, if any, this might be true; and asks how it might be that a Bayesian brain might, nonetheless, so poor at explicit probabilistic reasoning.

Dave Woods (University of Southampton)

Design of experiments for Generalised Linear (Mixed) Models

Generalised Linear and Generalised Linear Mixed Models (GLMs and GLMMs) may be used to describe data from a range of experiments in science, technology and industry. Example experiments with binary data come from areas such as crystallography, food science and aeronautical engineering. If the experiment is performed in blocks, eg subjects in a clinical trial or batches in manufacturing, a mixed model with random block effects allows the estimation of either subject-specific or population averaged treatment effects and induces an intra-block correlation structure for the response.

Finding optimal or efficient designs for GLMs and variants is complicated by the dependence of design performance on the values of the unknown model parameters. We describe methods for finding (pseudo) Bayesian designs that average a function of the information matrix across a prior distribution, and assess the resulting designs using simulation. The methods can also be extended to account for uncertainty in the linear predictor and link function, or to find designs for models with nonlinear predictors.

For GLMMs, the search for designs is complicated by the fact that the information matrix is not available in closed form. We make use of analytic and computational approximations, and also an alternative marginal model and generalised estimation equations.

Scott Schmidler (Duke University)

Bayesian Shape Matching for Protein Structure Alignment and Phylogeny

Understanding protein structure and function remains one of the great post-genome challenges of biology and molecular medicine. The 3D structure of a protein provides fundamental insights into its
biological function, mechanism, and interactions, and plays a key role in drug design. We have developed a Bayesian approach to modeling protein structure families, using methods adapted from the statistical
theory of shape. Our approach provides natural solutions to a variety of problems in the field, including pairwise and multiple alignment for the study of conservation and variability, algorithms for flexible
matching, and the impact of alignment uncertainty on phylogenetic tree reconstruction. Our recent efforts focus on extension to full evolutionary stochastic process models, which significantly improve upon
sequence-based phylogeny when divergence times are large.

Atanu Biswas (Indian Statistical Institute)

Comparison of treatments and data-dependent allocation for circular data from a cataract surgery

Circular data is a natural outcome in many biomedical studies, e.g. some measurements in ophthalmologic studies, degrees of rotation of hand or waist, etc. With reference to a real data set on astigmatism induced in two types of cataract surgeries we carry out some two-sample testing problems including the Behren-Fisher type of test in the circular set up. Response-adaptive designs are used in phase III clinical trials to allocate a larger proportion of patients to the better treatment. There is no available work on response-adaptive designs for circular data. Here we provide some response-adaptive designs where the responses are of circular nature, first an ad-hoc allocation design, and then an optimal design. Detailed simulation study and the analysis of the data set, including resigning the cataract surgery data, are carried out.

Joint work with Somak Dutta (University of Chicago), Arnab Kumar Laha (Indian Institute of Management, Ahmedabad), Partho Bakshi (Disha Eye Hospitals, Barrackpore, India).

Marek Kimmel, Rice University, Houston

Modeling the mortality reduction due to computed tomography screening for lung cancer

The efficacy of computed tomography (CT) screening for lung cancer remains controversial despite the fact that encouraging results from the National Lung Screening Trial are now available. In this study, the authors used data from a single-arm CT screening trial to estimate the mortality reduction using a modeling-based approach to construct a control comparison arm.

Hernando Ombao

Analysis of non-stationary time series

Hernando Ombao

Special topics on spectral analysis: principal components analysis, clustering and discrimination

Hernando Ombao

Intro to spectral analysis and coherence

Evsey Morozov (Karelian Research Centre, Russia)

Regenerative queues: stability analysis and simulation

We present a general approach to stability of regenerative queueing systems, which is based on the properties of the embedded renewal process of regenerations. Such a process obeys a useful characterization of the limiting remaining renewal time allowing in many cases to establish minimal stability conditions by a two-step procedure. At first step, a negative drift condition is used to prove that the basic process does not go to infinity (in probability), and at the second step, the finiteness of the mean regeneration period is proved. This approach has lead to the effective stability analysis of some models describing, in particular, such modern telecommunication systems as retrial queues and queues with optical buffers.

Moreover, we discuss regenerative simulation method including both classical and non-classical (extended) regeneration allowing a dependence between regeneration cycles.

Chris Nam (Warwick)
Quantifying the Uncertainty in Change Points in Time Series

Bryony Hill (Warwick)
A Gradient Field Approach to Modelling Fibre-Generated Spatial Point Processes

Ashley Ford (Warwick)
Indian Buffet Epidemics - A non-parametric Bayesian Approach to Modelling Heterogeneity

Sumeetpal Singh (Cambridge)

Computing the filter derivative using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a SMC algorithm to compute the derivative of the optimal filter in a Hidden Markov Model (HMM) and study its stability both theoretically and with numerical examples. Applications include calibrating the HMM from observed data in an online manner.

(Joint work with P. Del Moral and A. Doucet)

Alexander Gorban (Leicester)

Geometry of Data Sets

Plan
1. The problem
2. Approximation of multidimensional data by low-dimensional objects
2.1. Principal manifolds and elastic maps
2.2. Principal graphs and topological grammars
2.3. Three types of complexity: geometrical, topological and algorithmic
3. Self-simplification of essentially high-dimensional sets
4. Terra Incognita between low-dimensional sets and self-simplified high-dimensional ones.
5. Conclusion and open problems

Dr Sofia Massa (Oxford)

Combining information from graphical Gaussian models

In some recent applications, the interest is in combining information about relationships between variables from independent studies performed under partially comparable circumstances. One possible way of formalising this problem is to consider combination of families of distribution respecting conditional independence constraints with respect to a graph G, i.e., graphical models. In this talk I will introduce some motivating examples of the research question and I will present some relevant types of combinations and associated properties, in particular the relation between the properties of the combination and the structure of the graphs. Finally I will discuss some issues related to the estimation of the parameters of the combination.

Carlos Navarette (Universidad de La Serena)

Similarity analysis in Bayesian random partition models

This work proposes a method to assess the influence of individual observations in the clustering generated by any process that involves random partitions. It is called Similarity Analysis. It basically consists of decomposing the estimated similarity matrix into an intrinsic and an extrinsic part, coupled with a new approach for representing and interpreting partitions. Individual influence is associated with the particular ordering induced by individual covariates, which in turn provides an interpretation of the underlying clustering mechanism. Some applications in the context of Species Sampling Mixture Models will be presented, including Bayesian density estimation, dependent linear regression models and logistic regression for bivariate response. Additionally, an application to time series modelling based on time-dependent Dirichlet processes will be outlined.

Iain Murray (University of Edinburgh)

Sampling latent Gaussian models and hierarchical modelling

Sometimes hyperparameters of hierarchical probabilistic models are not well-specified enough to be optimized. In some scientific applications inferring their posterior distribution is the objective of learning.

Using a simple example, I explain why Markov chain Monte Carlo (MCMC) simulation can be difficult, and offer a solution for latent Gaussian models.

Wicher Bergsma (LSE) Marcel Croon, Jacques Hagenaars

Marginal Models for Dependent, Clustered, and Longitudinal Categorical Data

In the social, behavioural, educational, economic, and biomedical sciences, data are often collected in ways that introduce dependencies in the observations to be compared. For example, the same respondents are interviewed at several occasions, several members of networks or groups are interviewed within the same survey, or, within families, both children and parents are investigated. Statistical methods that take the dependencies in the data into account must then be used, e.g., when observations at time one and time two are compared in longitudinal studies. At present, researchers almost automatically turn to multi-level models or to GEE estimation to deal with these dependencies.

Despite the enormous potential and applicability of these recent developments, they require restrictive assumptions on the nature of the dependencies in the data. The marginal models of this talk provide another way of dealing with these dependencies, without the need for such assumptions, and can be used to answer research questions directly at the intended marginal level. The maximum likelihood method, with its attractive statistical properties, is used for fitting the models.

This talk is based on a recent book by the authors in the Springer series Statistics for the Social Sciences, see www.cmm.st.

Simon Spencer (Warwick)

Outbreak detection for campylobacteriosis in New Zealand

Identifying potential outbreaks of campylobacteriosis from a background of sporadic cases is made more difficult by the large spatial and temporal variation in incidence. One possible approach involves using Bayesian hierarchical models to simultaneously estimate spatial, temporal and spatio-temporal components of the risk of infection. By assuming that outbreaks are characterized by spatially localised periods of increased incidence, it becomes possible to calculate an outbreak probability for each potential disease cluster. The model correctly identifies known outbreaks in data from New Zealand for the period 2001 to 2007. Studies using simulated data have shown that by including epidemiological information in the model construction, this approach can outperform an established method.

Alberto Sorrentino (Warwick)

Bayesian filtering for estimation of brain activity in magnetoencephalography

Magnetoencephalography (MEG) is a sophisticated technique measuring the tiny magnetic fields produced by the brain activity. Relative to other functional neuroimaging techniques MEG recordings feature an outstanding temporal sampling resolution, in principle allowing for a study of the neural dynamics on a millisecond-by-millisecond time scale, but the spatial localization of neural currents from MEG data turns out to be an ill-posed inverse problem, i.e. a problem which has infinitely many solutions. To mitigate ill-posedness, a variety of parametric models of the neural currents are proposed in the burgeoning neuroimaging literature. In particular, under suitable approximations the problem of estimating brain activity from MEG data can be re-phrased as a Bayesian filtering problem with an unknown and time-varying number of sources.

In this talk I will first illustrate a statistical model of source localisation for MEG data which builds directly on the well-established Physics of the electro-magnetic brain field. The focus of the talk will then be to describe the application of a recently developed class of sequential Monte Carlo methods (particle filters) for estimation of the model parameters using empirical MEG data.

Jouni Kuha (London School of Economics)

Sample group means in multilevel models: Sampling error as measurement error

Research questions for models for clustered data often concern the effects of cluster-level averages of individual-level variables.  For example, data from a social survey might characterise neigborhoods in
terms of average income, ethnic composition etc. of people within each neighbourhood. Unless the true values of such averages are known from some other source, they are typically estimated by within-cluster
sample estimates, using data on the subjects in the observed data. This incurs a measurement error bias when these estimates are used as explanatory variables in subsequent modelling, even if the individual observations are measured without error. The measurement error variance can, however, be estimated from within-cluster variation, using knowledge of the sampling design within each cluster, and we can then apply relatively standard measurement error methods to adjust for the error. This talk considers such estimation for generalised linear mixed models, comparing common measurement error adjustments to naive analysis with no adjustment.

Tilman Davies (Massey University, NZ)

Refining Current Approaches to Spatial and Spatio-Temporal Modelling in Epidemiology

It is reasonable to expect both space and time to be important factors when investigating disease in human, animal and even plant populations. A common goal in many studies in geographical epidemiology, for example, is the idenification of disease risk 'hotspots', where spatial sub-regions that correspond to a statistically significant increase in the risk of infection are highlighted. More advanced problems involving not just space but space-time data, such as real-time disease surveillance, can be difficult to model due to complex correlation structures and computationally demanding operations. Decisions based on these kinds of analyses can range from the local, to national and even global levels. It is therefore important we continue to improve statistical methodology in this relatively young field, and ensure any theoretical benefits can flow through in practice.

This talk aims to give an overview of the PhD research currently underway in an effort to develop and implement refinements to spatial and spatio-temporal modelling. Of note include use of a spatially adaptive smoothing parameter for estimation of the kernel-smoothed relative-risk function, development of a novel, computationally inexpensive method for associated spatial tolerance contour calculation, release of an R package implementing these capabilities, and the scope for improvement to the current marginal minimum-contrast methods for parameter estimation in relevant stochastic models.

Ayanendranath Basu (Indian Statistical Institute)

Contamination Envelopes for Statistical Distances with Applications to Power Breakdown 
 
Inference procedures based on density based distances are known for their high efficiency and strong robustness. Similarly, other distance based analogues of the likelihood ratio test combine some of the properties of this test with good robustness properties. In this work we will derive general contamination envelopes for the distances under data contamination which have immediate application in deriving the power breakdown bounds for parametric tests of hypothesis based on density based distances. Our results will generalize and improve the existing power breakdown bounds for parametric tests based on distances. The talk will focus on the theoretical and computational issues related to this problem.

Matti Vihola (University of Jyväskylä)

On the stability and convergence of adaptive MCMC 

Adaptive MCMC algorithms tune the proposal distribution of the Metropolis-Hastings Markov kernel continuously using the simulated history of the chain. There are many applications where AMCMC algorithms are empirically shown to improve over the traditional MCMC methods. Due to the non-Markovian nature of the adaptation, however, the analysis of these algorithms requires more care than the traditional methods.

Most results on adaptive MCMC in the literature are based on assumptions that require the adaptation process to be `stable' (in a certain sense).

Such stability can rarely be established unless the process is modified by introducing specific stabilisation structures. The most straightforward strategy is to constrain the adaptation within certain pre-defined limits.

Such limits may sometimes be difficult to choose in practice, and the algorithms are generally sensitive to these parameters. In the worst case, poor choices can render the algorithms useless.

This talk focuses on the recent stability and ergodicity results obtained for adaptive MCMC algorithms without such constraints. The key idea behind the results is that the ergodic averages can converge even if the Markov kernels gradually `lose' their ergodic properties. The new approach enables to show some sufficient conditions for stability and ergodicity for random walk Metropolis algorithms: the seminal Adaptive Metropolis algorithm and an algorithm adjusting the scale of the proposal distribution based on the observed acceptance probability.  The results assume only verifiable conditions on the target distribution and the functional.

Andrew Grieve (King's College London)

Recent developments in Bayesian Adaptive design

2:30  Philip Dawid (University of Cambridge)

Local Proper Scoring Rules

A scoring rule S(x, Q) measures the quality of a quoted distribution Q for an uncertain quantity X in the light of the realised value x of X.  It is proper when it encourages honesty, i.e, when, if your uncertainty about X is represented by a distribution P, the choice Q = P minimises your expected loss. Traditionally, a scoring rule has been called local if it depends on Q only through q(x), the density of Q at x.  The only proper local scoring rule is then the log-score, -log q(x).  For the continuous case, we can weaken the definition of locality to allow dependence on a finite number m of derivatives of q at x.  A characterisation is given of such order-m local proper scoring rules, and their behaviour under transformations of the outcome space. In particular, any m-local scoring rule with m > 0 can be computed without knowledge of the normalising constant of the density. Parallel results for discrete spaces will be given.

3:30 - 4:00 Tea break

4:00  Christl Donnelly (Imperial College London)

Badger culling to control bovine TB: its potential role in a science-led policy

In 1997 the so-called Krebs Report recommended a randomized field trial be undertaken to evaluate the effectiveness of badger culling as a method of reducing bovine TB incidence in cattle herds.  The Randomised Badger Culling Trial was carried out in 30 100-sq-km areas. Along with related studies, it provided insights into several epidemiological aspects of the multi-species disease system.  The coalition government is currently seeking views on its proposal to include badger culling as a component of a science-led policy to control bovine TB.  

5:00 Reception to be held in Foyer A, Ruth Deech Building

Richard Gill (Leiden University)

Murder by numbers

In March 2003, Dutch nurse Lucia de Berk was sentenced to life imprisonment by a court in The Hague for 5 murders and 2 murder attempts of patients in her care at a number of hospitals where she had worked in the Hague between 1996 and 2001.  The only hard evidence against her was a statistical analysis resulting in a p-value of 1 in 342 million which purported to show that it could not be chance that so many incidents and deaths occured on her ward while she was on duty. On appeal in 2003 the life sentence was confirmed, this time for 7 murders and 3 attempts. This time, no statistical evidence was used at all: all the deaths were proven to be unnatural and Lucia shown to have caused them using scientific medical evidence only. However, after growing media attention and pressure by concerned scientists, including many statisticians, new forensic investigations were made which made showed that the conviction was unsafe. After a new trial, Lucia was spectacularly and completely exhonerated in 2010. 

I'll discuss the statistical evidence and show how it became converted into incontrovertible medical-scientific proof in order to secure the second, and as far as the Dutch legal system was concerned, definitive conviction. I'll also show how statisticians were instrumental in convincing the legal establishment that Lucia should be given a completely new trial. The history of Lucia de Berk brought a number of deficiencies to light in the way in which scientific evidence is evaluated in criminal courts. Similar cases to that of Lucia occur regularly all over the world. The question of how that kind of data should be statistically analyzed is still problematic. I believe that there are also important lessens to be learnt by the medical world, however, the Dutch medical community, where most people still believe Lucia is a terrible serial killer, is resisting all attempts to uncover what really happened.

Jianxin Pan (University of Manchester)

Joint modelling of mean and covariance structures for longitudinal data

When analysing longitudinal/correlated data, misspecification of covariance structures may lead to very inefficient estimators of parameters in the mean. In some circumstances, e.g., when missing data are present, it may result in biased estimators of the mean parameters. Hence, correct models for covariance structures play a very important role. Like the mean, covariance structures can be actually modelled using linear or nonlinear regression model techniques. A number of estimation methods were developed recently for modelling of mean and covariance structures, simultaneously. In this talk, I will review some methods on joint modelling of the mean and covariance structures for longitudinal data, including linear, non-linear regression models and semiparametric models. Real examples and simulation studies will be provided for illustration.

Sofia Olhede (UCL)

Estimation of Nonstationary Time Series

A time series is usually, unless a specific parametric model is assumed, understood from its first and second moments. If the process is also stationary, e.g. its first and second moments are invariant to time translations, then estimation is a mature and well-developed field.

Unfortunately, most observed processes are not stationary, as they are the result of the observation of transient phenomena. Therefore in classical time series analysis a theory has also been developed for the analysis of such processes. There are a number of short-comings of existing and well-developed methods, in particular in how the processes are allowed to evolve in time. I will discuss how to relax existing assumptions and still be able to develop good inference methods from a single time course of observations.

Richard Boys (Newcastle University)

Linking systems biology models to data: a stochastic kinetic model of p53 oscillations

This talk considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in this response, captured at the level of individual cells in a human cancer cell line. The primary goal of is to "calibrate" the model by finding parameters of the model (kinetic rate constants) that are most consistent with the experimental data. Significant amounts of prior information are available for the model parameters. It is therefore most natural to consider a Bayesian analysis of the problem, using sophisticated MCMC methods to overcome the formidable computational challenges.

Ajay Jasra (Imperial College London)

The Time Machine: A Simulation Approach for Stochastic Trees 

One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling  and sequential Monte Carlo techniques. The approach proceeds by simulating, backward in time from observed data, to a most recent common ancestor.

However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this talk I propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface.  The bias investigated from a theoretical point of view. Also, extensive simulation results are given, which justify the loss of accuracy with significant savings in computational time. This is a joint work with Maria De Iorio and Marc Chadeau-Hyam.

Timothy D. Johnson (University of Michigan)

Tim Johnson

Tim Johnson

Tim Johnson

Andrew Gelman (Columbia University)

Nothing is Linear, Nothing is Additive: Bayesian Models for Interactions in Social Science

Sujit Sahu (Southampton)

High Resolution Bayesian Space-Time Modelling for Ozone Concentration Levels

This talk will first discuss the two air quality standards for ozone levels and then will develop high resolution Bayesian space-time models which can be used to assess compliance. Predictive inference properties of several rival modelling strategies for both spatial interpolation and temporal forecasting will be compared and illustrated with simulation and real data examples. A number of large real life ozone concentration data sets observed over the eastern United States will also be used to illustrate the Bayesian space-time models. Several prediction maps from these models for the eastern US, published and used by the USEPA, will be discussed. 

Prof Adrian Bowman, University of Glasgow