AMSI Lecture tour: Rao-Blackwellisation of sampling schemes

Speaker: Christian Robert

Affiliation: Université Paris-Dauphine

Time: Tuesday 17/07/2012 from 10:30 to 11:30

Venue: Access Grid UWS. Presented from Parramatta (EB.1.32), accessible from Campbelltown (26.1.50) and Penrith (Y239).

Abstract:

Casella and Robert (1996, Biometrika) presented a general Rao-Blackwellisation principle for accept-reject and Metropolis-Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a potential high cost in computing and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis-Hastings based estimators while keeping the computing cost under control. The principle relates to the availability of an unbiased estimator of the acceptance probability. In a second if related part, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, those techniques do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable. Extensions to the random walk Metropolis--Hastings algorithm will also be discussed.

These are joint works with Randal Douc (Paristech-Telecom), available as http://arxiv.org/abs/0904.2144 v2 and Pierre Jacob (Paris-Dauphine & CREST) and Murray Smith (NIWA, NZ), available as http://arxiv.org/abs/1010.1595

Biography:

Christian is currently Professor in the Department of Applied Mathematics at the Université Paris-Dauphine since 2000. He is also a 2010-2015 senior member of the Institut Universitaire de France, and the former Head of the Statistics Laboratory of the Centre de Recherche en Économie et Statistique (CREST). He was Professor at the Université de Rouen from 1992 till 2000 and has held visiting positions in Purdue University, Cornell University, and the University of Canterbury, Christchurch, New-Zealand. He has been an adjunct professor at École Polytechnique for 13 years and is currently an adjunct professor in the Department of Mathematics and Statistics at the Queensland University of Technology (QUT), Brisbane, Australia.

Christian is a Fellow of the Royal Statistical Society and of the Institute of Mathematical Statistics (IMS), as well as a Medallion Lecturer of the IMS. He was Editor of the Journal of the Royal Statistical Society Series B from 2006 till 2009 and has been an associate editor of the Annals of Statistics, Journal of the American Statistical Society and Statistical Science. He is currently an Area Editor for the ACM Transactions on Modeling and Computer Simulation (TOMACS) journal and of Sankhya. He was the 2008 President of the International Society for Bayesian Analysis (ISBA).

His research areas cover Bayesian statistics, with a focus on decision theory and model selection, numerical probability, with works cantering on the application of Markov chain theory to simulation, and computational statistics, developing and evaluating new methodologies for the analysis of statistical models. He has written or co-written eight books on Bayesian statistics and computational methods, as well as over 150 research papers in these areas and their applications.