Abstract
Sequential Monte Carlo (SMC) methods for sampling from the posterior of static Bayesian models are flexible, parallelisable and capable of handling complex targets. However, it is common practice to adopt a Markov chain Monte Carlo (MCMC) kernel with a multivariate normal random walk (RW) proposal in the move step, which can be both inefficient and detrimental for exploring challenging posterior distributions. We develop new SMC methods with independent proposals which allow recycling of all candidates generated in the SMC process and are embarrassingly parallelisable. A novel evidence estimator that is easily computed from the output of our independent SMC is proposed. Our independent proposals are constructed via flexible copula-type models calibrated with the population of SMC particles. We demonstrate through several examples that more precise estimates of posterior expectations and the marginal likelihood can be obtained using fewer likelihood evaluations than the more standard RW approach.
Highlights
Sequential Monte Carlo (SMC, Chopin (2002); Del Moral et al (2006)) methods for static Bayesian models are naturally adaptive, parallelisable and are capable of dealing with targets that are multimodal or have complicated landscapes (see e.g. Del Moral et al (2006) and Cappe et al (2007))
We demonstrate that when independent proposals are used, all candidates generated in the SMC process can be used in evidence estimation and posterior inference
We have described a general method for forming these proposals based on modelling the marginals and the dependence separately, and the specific proposals applied here are based on modelling dependence through MGMMs
Summary
Sequential Monte Carlo (SMC, Chopin (2002); Del Moral et al (2006)) methods for static Bayesian models are naturally adaptive, parallelisable and are capable of dealing with targets that are multimodal or have complicated landscapes (see e.g. Del Moral et al (2006) and Cappe et al (2007)). The move step is commonly chosen to be several iterations of a Markov chain Monte Carlo (MCMC, Metropolis et al (1953)) kernel, often with a random walk proposal Despite their commonplace use, random walk proposals can be inefficient at exploring the target and this can have a detrimental effect on evidence and posterior expectation estimates. We propose a novel evidence estimator which is simple and computationally efficient to calculate from our independent SMC output These new recycling schemes for SMC can lead to increases in the effective sample size (ESS) targeting the posterior, improved sampling from complex posterior distributions and significant variance reductions when compared to no recycling and the recycling method of Nguyen et al (2014).
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