On population-based simulation for static inference

Abstract

In this paper we present a review of population-based simulation for static inference problems. Such methods can be described as generating a collection of random variables {X n } n=1,?,N in parallel in order to simulate from some target density ? (or potentially sequence of target densities). Population-based simulation is important as many challenging sampling problems in applied statistics cannot be dealt with successfully by conventional Markov chain Monte Carlo (MCMC) methods. We summarize population-based MCMC (Geyer, Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156---163, 1991; Liang and Wong, J. Am. Stat. Assoc. 96, 653---666, 2001) and sequential Monte Carlo samplers (SMC) (Del Moral, Doucet and Jasra, J. Roy. Stat. Soc. Ser. B 68, 411---436, 2006a), providing a comparison of the approaches. We give numerical examples from Bayesian mixture modelling (Richardson and Green, J. Roy. Stat. Soc. Ser. B 59, 731---792, 1997).