Empirically Comparing the Performance of Local MCMC Algorithms with Pools of Proposals

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Mylène Bédard*+
• Companies: Université De Montréal
• Keywords: computational cost ; delayed rejection ; Metropolis-Hastings ; multiple-try ; regression

Abstract

To improve on the Metropolis algorithm, various MCMC methods with pools of proposals, such as the multiple-try and delayed rejection Metropolis algorithms, have been proposed. These methods generate several candidates in a single iteration; accordingly they are computationally more intensive than the Metropolis algorithm. It is usually difficult to provide a general estimate for the computational cost of a method without being overly conservative; potentially efficient methods could thus be overlooked by relying on such estimates. In this talk, we describe three algorithms with pools of proposals - the multiple-try Metropolis (MTM) algorithm, the MTM hit-and-run algorithm, and the delayed rejection Metropolis algorithm with antithetic proposals (DR-A) - and investigate the net performance of these samplers in various contexts. To allow for a fair comparison, the study is carried under optimal mixing conditions for each of these samplers. The algorithms are used in the contexts of Bayesian logistic regressions and classical inference for a linear regression model. This talk is based on work in collaboration with M. Mireuta, E. Moulines, and R. Douc.