Abstracts TT2010
Week 1 - April 29 - CANCELLED
Rolf Sundberg (Stockholm University, Mathematical Statistics)
Title: Flat and multimodal likelihoods and mode lack of fit in curved exponential families
Abstract:
Week 2 - May 6
Arnaud Doucet (UBC Computer Science)
Title: Forward Smoothing using Sequential Monte Carlo with Application to Recursive Parameter Estimation
Abstract: 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 new SMC algorithm to compute the expectation of additive functionals recursively. Compared to the standard path space SMC estimator whose asymptotic variance increases quadratically with time even under favourable mixing assumptions, the asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation in state-space models using SMC algorithms which do not not suffer from the particle path degeneracy problem.
Joint work with P. Del Moral (INRIA Bordeaux) & S.S. Singh (Cambridge University):
Week 3 - May 13
NO SEMINAR
Title:
Abstract:
Week 4 - May 20
Ruth Salway (Bath, Department of Mathematics and Statistics)
Title: A Hybrid Model for Reducing Aggregation Bias Using Small Samples of Individual Data
Abstract: In environmental and social epidemiology, studies that use aggregate data (such as area-level disease rates and average exposure to some risk factor) are often used to make inference about individual health risks. A major problem is difficulty in interpretation: area level estimates are not equivalent to individual level estimates, but are subject to aggregation bias. To recover the individual risks we need samples of individual exposure data within each area; unfortunately these may be difficult or expensive to obtain, particularly if large samples are required.
In this talk I will describe a new model suitable for use with small samples of individual data. Prior information is incorporated in the form of a Bayesian non-parametric Dirichlet process prior, and combined with an estimating functions approach to inference. The model is illustrated with data on lung cancer mortality and exposure to residential radon.
Week 5 - May 27
John Moriarty (Manchester Departments of Mathematics and Statistics)
Title: Evolutionary Inference for Functional Data: Placing Gaussian Processes on Phylogenies
Abstract: I will discuss a natural construction for Gaussian processes on phylogenies, intended for nonparametric evolutionary inference on rich ancestral data objects such as continuous curves. A modified covariance function will be given that corrects for the relationships between states at different points on a phylogeny, and its use in inference will be discussed. In general this covariance is expressed via the solution of an integral equation although, for a given Gaussian process, a set of solutions sufficient for all phylogenies may be precomputed as a library which, for stationary processes, is one dimensional. This work has relevance for inference on functional data objects related by an evolutionary process; it also specifies a class of hierarchical clustering algorithms for functional data objects. Joint work with Nick Jones (Oxford).
Week 6 - June 3 - CANCELLED
Jon Williamson, Department of Philosophy, University of Kent
Title: Connections between Bayesian philosophy and statistics
Abstract: The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed - two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly. This view turns out to be rather natural if Bayesianism is seen as primarily addressing a philosophical question concerning strength of belief rather than a statistical question.
Week 7 - June 10
Graduate presentations
Week 8 - June 17
Mark Steel, (Department of Statistics, University of Warwick)
Title: Stick-Breaking Autoregressive Processes
Abstract: This paper considers the problem of defining a time-dependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form.
The processes with Poisson-Dirichlet and Dirichlet process marginals are investigated in some detail. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the marginal stick-breaking process are nondecreasing sequences. We derive a generalized P´ olya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. We apply the proposed methods to financial data to develop a semi-parametric stochastic volatility model with a time-varying nonparametric returns distribution. Finally, we present two examples concerning the analysis of regional GDP and its growth.
joint work with J.E. Griffin
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