Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling

Authors:
Radu V. Craiu;Christiane Lemieux
Affiliations:
Department of Statistics, University of Toronto, Toronto, Canada;Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada N2L 3G1
Venue:
Statistics and Computing
Year:
2007

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Abstract

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensional spaces and can be used easily when the proposal distribution is Gaussian. We explore the use of quasi Monte Carlo (QMC) methods to generate highly stratified samples. A series of examples is presented to evaluate the potential of the method.