Sequential Monte Carlo for Bayesian Computation

Sequential Monte Carlo (SMC) methods are a class of importance sampling and resampling techniques designed to simulate from a sequence of probability distributions. These approaches have become very popular over the last few years to solve sequential Bayesian inference problems (e.g. Doucet et al. 2001). However, in comparison to Markov chain Monte Carlo (MCMC), the application of SMC remains limited when, in fact, such methods are also appropriate in such contexts (e.g. Chopin (2002); Del Moral et al. (2006)). In this paper, we present a simple unifying framework which allows us to extend both the SMC methodology and its range of applications. Additionally, reinterpreting SMC algorithms as an approximation of nonlinear MCMC kernels, we present alternative SMC and iterative self-interacting approximation (Del Moral and Miclo 2004; 2006) schemes. We demonstrate the performance of the SMC methodology on static and sequential Bayesian inference problems.