AMSI Lecturer: Rao-Blackwellisation of sampling schemes

Host Institution:

University of Western Sydney

Title of Seminar:

Rao-Blackwellisation of sampling schemes

Speaker's Name:

Professor Christian Robert

Speaker's Institution:

Université Paris-Dauphine

Time and Date:

Tuesday 17 July 2012, 10:30am (AEST)

Seminar 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

A related presentation is available as http://www.slideshare.net/xianblog/talk-in-telecomparis-nov-15-2011

This talk is part of the 2012 AMSI Lecture tour. For further details of the tour, please visit www.amsi.org.au/robert.php

Seminar Convenor:

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