Antonio Lijoi

OXFORD-WARWICK JOINT SEMINAR

Prof Odd Aalen, Dept of Biostatistics, University of Oslo (3-4pm Rm L4, Science Concourse Main Level)
Statistics, causality and dynamic path modelling

Prof Geert Molenberghs, Centre for Statistics, Hasselt University, Belgium (4.30-5.30 Rm LIB1, Library)
Model assessment and sensitivity analysis when data are incomplete

Abstracts

Prof Wilfrid Kendall, University of Warwick
Short-length routes in low-cost networks via Poisson line patterns (joint work with David Aldous)

How efficiently can one move about in a network linking a configuration of n cities? Here the notion of "efficient" has to balance (a) total network length against (b) short network distances between cities. My talk will explain how to use Poisson line processes to produce networks which are nearly of shortest total length, which make the average inter-city distance almost Euclidean.

Dr Alex Schmidt, Instituto de Matematica - UFRJ, Brazil
Modelling multiple series of runoff:  The case of Rio Grande Basin (joint work with Romy R Ravines and Helio S Migon)

This paper proposes a joint model for the rainfall and multiple series of runoff at a basin, two of the most important hydrological processes.  The proposed model takes into account the different spatial units in which these variables are measured, and as a natural benefit its parameters have physical interpretations. Also, we propose to model runoff and rainfall in their original scales, making no use of any transformation to reach normality of the data. More specifically, our proposal follows Bayesian dynamic nonlinear models through the use of transfer function models.  The resultant posterior distribution has no analytical solution and stochastic simulation methods are needed to obtain samples from the target istribution.  In particular, as the parameters of the dynamic model are highly correlated, we make use of the Conjugate Updating Backward Sampling recently proposed by Ravines, Migon and Schmidt (2007), in order to efficiently explore the space of the parameters. We analyze a sample from a basin located in the Northeast of Brazil, the Rio Grande Basin. The data consist of monthly recorded series from January 1984 to September 2004, at three runoff stations and nine rainfall monitoring stations, irregularly located in an area of drainage of 37,500 sq km. Model assessment, spatial interpolation and temporal predictions are part of our analysis. Results show that our approach is a promising tool for the runoff-rainfall analysis.

Prof Valentine Genon-Catalot, Paris 5
Explicit filtering of discretized diffusions

Consider a pair signal-observation ((x_n, y_n), n > 0) where the unobserved signal (x_n) is a Markov chain and the observed component is such that, given the whole sequence (x_n), the random variables (y_n) are independent and the conditional distribution of y_n only depends on the corresponding state variable x_n.  Concrete problems raised by these observations are the prediction, filtering or smoothing of (x_n).  This requires the computation of the conditional distributions of x_l given y_n, . . . , y_1, y_0 for all l, n.  We introduce sufficient conditions allowing to obtain explicit formulae for these conditional distributions and extend the notion of finite dimensional filters using mixtures of distributions.  The method is applied to the case where the signal x_n = Xn_ is a discrete sampling of a one dimensional diffusion process: Concrete models are proved to fit in our conditions.  Moreover, for these models, exact likelihood inference based on the observation (y_0, . . . , y_n) is feasible.

Dr Daniel Farewell, Cardiff University
Simple models for informatively censored longitudinal data

Models for longitudinal measurements truncated by possibly informative dropout have tended to be either mathematically complex or computationally demanding. I will review an alternative recently proposed in our RSS discussion paper (Diggle et al. 2007), using simple ideas from event-history analysis (where censoring is commonplace) to yield moment-based estimators for balanced, continuous longitudinal data. I shall then discuss  some work in progress: extending these ideas to more general longitudinal data, while maintaining simplicity of understanding and implementation.

Prof Gareth Roberts, University of Warwick (Joint Statistics/Econometrics Seminar)
This presentation will review recent work in the area of Bayesian inference for discretely (and partially) observed diffusion. I will concentrate on Bayesian approaches which necessitate the use of Markov chain Monte Carlo techniques, and the talk will consider the problem of MCMC algorithm design. The approach will be presented in a continuous-time framework.

Dr Sumeet Singh, Signal Processing Laboratory, Cambridge
Filters for spatial point processes

We consider the inference of a hidden spatial Point Process (PP) X on a CSMS (complete separable metric space) X, from a noisy observation y modeled as the realisation of another spatial PP Y on a CSMS Y. We consider a general model for the observed process Y which includes thinning and displacement and characterise the posterior distribution of X for a Poisson and Gauss-Poisson prior.  These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of X considered are general enough for many arget Tracking applications,  which is an important study area in Engineering. Accompanying numerical implementations based on Sequential Monte Carlo will be presented.

Professor Malcolm Faddy, Queensland University of Technology, Australia
Analysing hospital length of stay data: models that fit, models that don’t and does it matter?

Hospital length of stay data typically show a distribution with a mode near zero and a long right tail, and can be hard to model adequately. Traditional models include the gamma and log-normal distributions, both with a quadratic variance-mean relationship. Phase-type distributions which describe the length of time to absorption of a Markov chain with a single absorbing state also have a quadratic variance-mean relationship. Covariates of interest include an estimate of the length of stay for an uncomplicated admission, with excess length of stay modelled relative to this quantity either multiplicatively or additively. A number of different models can therefore be constructed, and the results of fitting these models will be discussed in terms of goodness of fit, significance of covariate effects and estimation of quantities of interest to health economists.

Dr Elena Kulinskaya, Statistical Advisory Service, Imperial College
Meta analysis on the right scale

This talk is about an approach to meta analysis and to statistical evidence developed jointly with Stephan Morgenthaler and Robert Staudte, and now written up in our book 'Meta Analysis: a guide to calibrating and combining statistical evidence'  to be published by Wiley very soon. The traditional ways of measuring evidence, in particular with p-values, are neither intuitive nor useful when it comes to making comparisons between experimental results, or when combining them. We measure evidence for an alternative hypothesis, not evidence against a null. To do this, we have in a sense adopted standardized scores for the calibration scale. Evidence for us is simply a transformation of a test statistic S to another one (called evidence T=T(S)) whose distribution is close to normal with variance 1, and whose mean grows from 0 with the parameter as it moves away from the null. Variance stabilization is used to arrive on this scale. For meta analysis the results from different studies are transformed to a common calibration scale, where it is simpler to combine and interpret them. 

Dr Richard Samworth, Statistical Laboratory, Cambridge
Computing the maximum likelihood estimator of a multidimensional log-concave density

We show that if $X_1,...,X_n$ are a random sample from a log-concave density $f$ in $\mathbb{R}^d$, then with probability one there exists a unique maximum likelihood estimator $\hat{f}_n$ of $f$.  The use of this estimator is attractive because, unlike kernel density estimation, the estimator is fully automatic, with no smoothing parameters to choose. The existence proof is non-constructive, however, and in practice we require an iterative algorithm that converges to the estimator.  By reformulating the problem as one of non-differentiable convex optimisation, we are able to exhibit such an algorithm.  We will also show how the method can be combined with the EM algorithm to fit finite mixtures of log-concave densities.  The talk will be illustrated with pictures from the R package LogConcDEAD.

This is joint work with Madeleine Cule (Cambridge), Bobby Gramacy (Cambridge) and Michael Stewart (University of Sydney).

Dr Robert Gramacy, Statistical Laboratory Cambridge
Importance Tempering
Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density pi(theta).  The technique involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say pi_k(theta) = pi(theta)^k.  Small values of k encourage better mixing, but samples from pi are only obtained when the joint chain for (theta,k) reaches k=1. However, the entire chain can be used to estimate expectations under pi of functions of interest, provided that importance sampling (IS) weights are calculated.  Unfortunately this method, which we call importance tempering (IT),  has tended not work well in practice.  This is partly because the most immediately obvious implementation is naive and can lead to high variance estimators.  We derive a new optimal method for combining multiple IS estimators and prove that this optimal combination has a highly desirable property related to the notion of effective sample size.  The methodology is applied in two modelling scenarios requiring reversible-jump MCMC, where the naive approach to IT fails: model averaging in treed models, and model selection for mark--recapture data. 

Professor Simon Wood, University of Bath
Generalized Additive Smooth Modelling
Generalized Additive Models are GLMs in which the linear predictor is made up, partly, of a sum of smooth functions of predictor variables. I will talk about the penalized regression spline approach to GAM, as implemented, for example, in R package mgcv. In particular I will focus on two interesting aspects: low rank representation of smooth functions of several covariates and stable computation of both model coefficients and smoothing parameters. More than half the slides will have pictures.
 

Terry Speed, University of California, Berkeley
Alternative Splicing in Tumors: Detection and Interpretation
In this talk I will discuss using the Affymetrix GeneChip Human Exon and Human Gene 1.0 ST arrays for the detection of genes spliced differently in some tumors in comparison with others. I plan to begin by introducing the arrays and the expression data they produce. Next I will outline the way in which we use such data in our attempts to identify exon-tumor combinations exhibiting splicing patterns different from the majority. This will be illustrated by examples from publicly available tissue and mixture data. Then I will briefly discuss some of the additional issues which arise when we seek to enumerate such alternative splicing patterns on a genome-wide scale. Finally, I will exhibit some of the results we have found applying these methods to glioblastoma tissue samples collected as part of The Cancer Genome Atlas (TCGA) project. (This is joint work with ELizabeth Purdom, Mark Robinson, Ken Simpson, and members of the Berkeley Cancer Genome Center.)

Alexey Koloydenko & Juri Lember (Joint Talk), University of Nottingham
Adjusted Viterbi Training for Hidden Markov Models
The Expectation Maximisation (EM) procedure is a principal tool for parameter estimation in hidden Markov models (HMMs). However, in applications EM is sometimes replaced by Viterbi training, or extraction, (VT). VT is computationally less intensive and more stable, and has more of an intuitive appeal, but VT estimation is biased and does not satisfy the following fixed point property: Hypothetically, given an infinitely large sample and initialized to the true parameters, VT will generally move away from the initial values. We propose adjusted Viterbi training (VA), a new method to restore the fixed point property and thus alleviate the overall imprecision of the VT estimators, while preserving the computational advantages of the baseline VT algorithm. Simulations show that VA indeed improves estimation precision appreciably in both the special case of mixture models and more general HMMs.

We will discuss the main idea of the adjusted Viterbi training. This will also touch on tools developed specifically to analyze asymptotic behaviour of maximum a posteriori (MAP) hidden paths, also known as Viterbi alignments. Our VA correction is analytic and relies on infinite Viterbi alignments and associated limiting probability distributions. While explicit in the special case of mixture models, these limiting measures are not obvious to exist for more general HMMs. We will conclude by presenting a result that under certain mild conditions, general (discrete time) HMMs do possess the limiting distributions required for the construction of VA. 

Prof Antony Pettitt, Lancaster University
Statistical inference for assessing infection control measures for the transmission of pathogens in hospitals
Patients can acquire infections from pathogen sources within hospitals and certain pathogens appear to be found mainly in hospitals.  Methicillin-resistant Staphylococcus Aureus (MRSA) is an example of a hospital acquired pathogen that continues to be of particular concern to patients and hospital management.  Patients infected with MRSA can develop severe infections which lead to increased patient morbidity and costs for the hospital.  Pathogen transmission to a patient can occur via health-care workers that do not regularly perform hand hygiene.  Infection control measures that can be considered include isolation for colonised patients and improved hand hygiene for health-care workers.
The talk develops statistical methods and models in order to assess the effectiveness of the two control measures (i) isolation and (ii) improved hand hygiene.  For isolation, data from a prospective study carried out in a London hospital is considered and statistical models based on detailed patient data are used to determine the effectiveness of isolation.  The approach is Bayesian. For hand hygiene it is not possible, for ethical and practical reasons, to carry out a prospective study to investigate various levels of hand hygiene.  Instead hand hygiene effects are investigated by simulation using parameter values estimated from data on health-care worker hand hygiene and weekly colonisation incidence collected from a hospital ward in Brisbane.  The approach uses profile likelihoods.Both approaches involve transmission parameters where there is little information available and contrasting compromises have to be made. Conclusions about the effectiveness of the two infection control measures will be discussed. The talk involves collaborative work with Marie Forrester, Emma McBryde, Chris Drovandi, Ben Cooper, Gavin Gibson, Sean McElwain.

Alastair Young, Imperial College London
Objective Bayes and Conditional Inference
In Bayesian parametric inference, in the absence of subjective prior information about the parameter of interest, it is natural to consider use of an objective prior which leads to posterior probability quantiles which have, at least to some higher order approximation in terms of the sample size, the correct frequentist interpretation. Such priors are termed probability matching priors. In many circumstances, however, the appropriate frequentist inference is a conditional one. The key contexts involve inference in multi-parameter exponential families, where conditioning eliminates the nuisance parameter, and models which admit ancillary statistics, where conditioning on the ancillary is indicated by the conditionality principle of inference. In this talk, we consider conditions on the prior under which posterior quantiles have, to high order, the correct conditional frequentist interpretation. The key motivation for the work is that the conceptually simple objective Bayes route may provide accurate approximation to more complicated frequentist procedures. We focus on the exponential family context, where it turns out that the condition for higher order conditional frequentist accuracy reduces to a condition on the model, not the prior: when the condition is satisfied, as it is in many key situations, any first order probability matching prior (in the unconditional sense) automatically yields higher order conditional probability matching. We provide numerical illustrations, discuss the relationship between the objective Bayes inference and the parametric bootstrap, as well as giving a brief account appropriate to the ancillary statistic context, where conditional frequentist probability matching is more difficult. [This is joint work with Tom DiCiccio, Cornell].