Sequential Monte Carlo Samplers

Abstract

We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of normalizing constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference. Copyright 2006 Royal Statistical Society.

Graph Matching via Sequential Monte Carlo

“…The samples x (i) t at time t are generated from the importance distribution η t , which is constructed by a Markov transition kernel K and the previous distribution π t−1 [24]; each sample x (i) t evolves from x (i) t−1 according to the kernel K, and the importance distribution η t is represented by…”

“…To formulate graph matching in the SMC framework, we introduced a sequence of intermediate distributions [24], which starts from a simple initial distribution and gradually moves toward the final target distribution equivalent to the objective function of (1). This SMC procedure performs graph matching by sequentially re-distributing particles over the evolving sample space according to the intermediate target distribution at each step.…”

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

“…We therefore refer to this as the ABC-PMC algorithm. There is also a wider family of related ABC-SMC algorithms, including Sisson et al (2007) and Del Moral et al (2012), which update their particles in more complex ways based on MCMC moves, as described in Del Moral et al (2006). (c) Simulate dataset D * from the model using parameters θ * .…”

Population-Based Reversible Jump Markov Chain Monte Carlo

“…We remark that methods other than MCMC may be used for difficult simulation problems, such as sequential Monte Carlo (e.g. Del Moral et al, (2006)), but such methods are not the focus of this paper.…”