On population-based simulation for static inference

Abstract

In this paper we present a review of populationbased 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 π (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).

Estimating Bayes factors via thermodynamic integration and population MCMC

“…This is in contrast with suggestions made by Jasra et al (2007), who advise that a uniform tempering schedule is generally a good choice when running population-based simulations. There are differences, however, in the criteria used for determining how well a temperature schedule performs, which may account for the drastic difference in conclusions.…”

“…As previously mentioned, a possible solution to this sampling problem is available through the use of population MCMC methods, see e.g. (Iba, 2000;Liang and Wong, 2001;Laskey and Myers, 2003;Jasra et al, 2007). Such population MCMC methods can be very efficient in the context of model comparison because not only do they allow sampling from highly nonlinear multimodal posterior distributions, but the usually redundant samples taken from intermediate temperatures may also be reused in the estimation of the marginal likelihood using thermodynamic integration (Friel and Pettitt, 2008).…”

Abnormal Object Detection by Canonical Scene-Based Contextual Model

“…This paper adopts a sampling method, which is called Pop-MCMC [8], to solve the optimization problem (3). Pop-MCMC generates multiple samples, also called chromosomes, from multiple Markov chains in parallel.…”

“…We use a population-based Markov Chain Monte Carlo (Pop-MCMC) technique [8] to predict the existence of abnormal objects via the proposed model. This technique generates samples from multiple, dependent chains, resulting in a high mixing rate.…”

Stereo Matching Using Population-Based MCMC

“…In this paper, we propose a new MCMC method called Population-Based MCMC (Pop-MCMC) (Liang and Wong 2000;Jasra and Stephens 2007) that can overcome the drawbacks of SWC for stereo matching problem. Our goal is to obtain the lower energy state faster than other sampling methods including SWC which have been previously applied to this problem.…”