Terms 1-3, Location MB0.08, Fridays 12:15-14:00 (12:15-12:45 is an informal sandwich lunch).
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2019/20 Term 1:
- Week 1 - 4th October - Felipe Medina Aguayo (Reading) - "Revisiting the balance heuristic for estimating normalising constants"
- Abstract: Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in computer graphics. The basic ingredients for computing the estimator are: a set of proposal distributions, indexed by some discrete label, and a predetermined number of draws from each of these proposals. However, if the number of available proposals is much larger than the number of permitted importance points, one needs to select, possibly at random, which of these distributions will be used. We explore some improvements and variations of the balance heuristic via a novel extended-space representation of the estimator, leading to straightforward annealing schemes for variance reduction purposes. We will also look at the intractable scenario where the proposal density is only available as a joint function with the discrete label, as may be encountered in problems where an ordering is imposed.
- Week 2 - 11th October - cancelled (OxWaSP workshop)
- Week 3 - 18th October - Alice Corbella (Warwick) - "Pseudo Marginal methods in practice: Inferring epidemics from multiple dependent data"
The evolution of an epidemic can be represented as a non-linear dynamical system, combining a transmission model, approximating the unobserved infection process, with further stochastic models for the development and detection of symptoms.
Pseudo Marginal methods (Andrieu and Roberts 2009) provide a useful tool for the inference in dynamic system where the likelihood can be estimated by (sequential) Monte Carlo methods.
We formulate a model for Influenza dynamics in England when multiple, dependent data are available. We also propose a Monte Carlo estimate of the likelihood and use it in a Pseudo Marginal framework. We also present a misspecified model that does not account for dependence between data sources, leading to direct computation of the likelihood. We compare via simulation the inference in the two cases showing that when the dependence is disregarded, this leads to over-efficient estimates.
Lastly, we present an analysis of real data, proving the usefulness of our model and the inference.
- Week 4 - 25th October - Lionel Riou-Durand (Warwick) - "Noise contrastive estimation: Asymptotic properties, formal comparison with MC-MLE"
- A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation), and NCE (noise contrastive estimation); both methods rely on simulating artificial data-points to approximate the normalising constant. While the asymptotics of MC-MLE have been established under general hypotheses (Geyer, 1994), this is not so for NCE. We establish consistency and asymptotic normality of NCE estimators under mild assumptions. We compare NCE and MC-MLE under several asymptotic regimes. In particular, we show that, when m goes to infinity while n is fixed (m and n being respectively the number of artificial data-points, and actual data-points), the two estimators are asymptotically equivalent. Conversely, we prove that, when the artificial data-points are IID, and when n goes to infinity while m/n converges to a positive constant, the asymptotic variance of a NCE estimator is always smaller than the asymptotic variance of the corresponding MC-MLE estimator. We illustrate the variance reduction brought by NCE through a numerical study.
- Week 5 - 1st November - Anthony Mulholland (Bristol) - "Material Map Inversion of Complex and Locally Anisotropic Media for Improved Imaging in Non-Destructive Testing"
Imaging defects in austenitic welds presents a significant challenge for the ultrasonic non-destructive testing community. Due to the heating process during their manufacture, a polycrystalline structure develops, where large grains with locally anisotropic properties cause the ultrasonic waves to scatter and refract. When basic imaging algorithms which make straight ray and constant wave speed assumptions are applied to datasets arising from the inspection of these welds, the resulting defect reconstructions are often distorted and difficult to interpret correctly. Knowledge of the underlying material microstructure would allow correction of the expected wave travel times (on which time-domain imaging algorithms are typically based) and thus result in more reliable defect reconstructions. In this talk, an approximation to the underlying, locally anisotropic structure of the weld is constructed from ultrasonic phased array inspection data. A new forward model of wave front propagation in locally anisotropic media, the Anisotropic Multi-Stencil Fast Marching Method, is presented and used within the reversible-jump Markov chain Monte Carlo method to invert for the map of regional crystal orientations. This forward model and estimated map are then used as the basis for an imaging algorithm and the resulting reconstructions of defects embedded within these polycrystalline materials are used to measure the success of the approach. Receiver operating characteristic curves are then calculated to demonstrate the enhanced probability of detection achieved when the material map is accounted for and it is shown that the reconstructed material maps can significantly increase the probability of detection of defects in the far field.
- Week 6 - 8th November - Kathryn Leeming (Warwick) - "Local white noise testing using wavelets"
In this talk we motivate a local white noise test, testing for structure in observations or residuals at a local level, rather than globally. For this test we do not wish to make the assumption of Gaussian noise. Wavelets are shown to be a natural candidate for creating such a test, and an introduction to wavelets for statistical signal processing will be provided. Properties of the wavelet spectrum such as covariance and asymptotic distribution will be shown, enabling the local white noise test to be evaluated. Our local white noise test is compared in simulations to classical white noise tests, and its use is demonstrated on residuals of a time series. (Joint work with Guy Nason).
- Week 7 - 15th November - Nikolas Kantas (Imperial) - "Parameter estimation and sensor placement for the stochastic advection diffusion equation"
The talk is on performing inference for dissipative SPDE models using observations obtained by possibly a large number of sensors. This setup is relevant in applications such as environmental monitoring, numerical weather prediction, geosciences and more. When the model parameters (of the SPDE and sensors) are known approximating conditional probability laws given observations (i.e. filter distributions) is possible for non-linear SPDE models using elaborate and expensive particle methods or using heuristics such as the EnKF. The question we would like to pose in this talk is how to estimate model parameters and how to place sensor optimally to minimise uncertainty in our filter estimates. We will focus only on the linear Gaussian case and in particular the stochastic advection diffusion equation. This is work in progress jointly with Louis Sharrock (Imperial).
- Week 8 - 22nd November - Chris Sherlock (Lancaster) - "Fast, exact inference for discretely observed Markov jump processes using finite rate matrices"
We consider inference for a discretely observed Markov jump process with an infinite statespace, such as occurs in biological and environmental systems. When the statespace is finite, inference for the resulting continuous-time Markov chain using its rate matrix is straightforwards, but in the case of an infinite state space the method of choice is particle MCMC. We provide a new method, the minimal extended statespace algorithm (MESA) for exact Bayesian inference, that uses finite-dimensional rate matrices even though the statespace is infinite. In contrast to particle MCMC, MESA is most efficient when there is no observation noise, and becomes gradually less efficient as the observation noise increases.
- Week 9 - 29th November - cancelled (instead, please attend the Dept Colloquium by Terry Lyons (Oxford) in MS.02, 2-3pm on Tuesday 26th November)
- Week 10 - 6th December - Martina Favero (KTH Stockholm) - "Weak convergence for a sequence of coalescent processes"
We show weak convergence for a sequence of Markov chains constituted by the block counting process of the Kingman coalescent with parent independent mutations and by the process counting the corresponding number of mutations, as the sample size goes to infinity. Time is scaled and convergence of semigroups is proved. The limiting process consists of a deterministic part and of conditionally independent Poisson processes with varying intensity.We explain how this result may be used to study the asymptotic efficiency of importance sampling algorithms on the coalescent with parent dependent mutations, and to determine the asymptotic behaviour of the sampling probabilities. This is a work in progress with H.Hult (KTH)
2019/20 Term 2:
- Week 1 - 10th January -
- Week 2 - 17th January - Alex Buchholz (Cambridge)
- Week 3 - 24th January - Sam Livingstone (UCL)
- Week 4 - 31st January - Brieuc Lehmann (Oxford)
- Week 5 - 7th February - Ioannis Kosmidis (Warwick)
- Week 6 - 14th February - Dennis Prangle (Newcastle)
- Week 7 - 21st February - Alisa Kirichenko (Oxford)
- Week 8 - 28th February - cancelled (instead, please attend the Dept Colloquium by Judith Rousseau (Oxford) in OC0.03, 2-3pm on Tuesday 25th February)
- Week 9 - 6th March - Francesca Crucinio (Warwick)
- Week 10 - 13th March - Letizia Angeli (Warwick)
2019/20 Term 3:
- Week 1 - 24th April -
- Week 2 - 1st May -
- Week 3 - 8th May - cancelled (instead, please attend the Dept Colloquium)
- Week 4 - 15th May -
- Week 5 - 22nd May - Helen Ogden (Southampton)
- Week 6 - 29th May -
- Week 7 - 5th June - Ruth Baker (Oxford)
- Week 8 - 12th June -
- Week 9 - 19th June -
- Week 10 - 26th June -
Some key phrases:
- Sampling and inference for diffusions
- Exact algorithms
- Intractable likelihood
- Pseudo-marginal algorithms
- Particle filters
- Importance sampling
- Adaptive MCMC
- Perfect simulation
- Markov chains...
- Random structures...
- Randomised algorithms...