On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm introduced by Liu (2001), termed SMC sampler PRC, and show that this variant can be considered under the same framework of the sequential Monte Carlo sampler of Del Moral et al. (2006). We make connections with existing algorithms and theoretical results, and extend some theoretical results to the SMC sampler PRC setting. We examine the properties of the SMC sampler PRC and give recommendations for user specified quantities. We also study the special case of SMC sampler PRC in the “likelihood free” approximate Bayesian computation framework, as introduced by Sisson et al. (2007).