Sequential Monte Carlo samplers with independent Markov chain Monte Carlo proposals

<I>Sequential Monte Carlo</I> (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 to the ability to explore challenging posterior distributions. We propose a flexible copula-type independent proposal which uses the population of particles to adapt the kernel in a more sophisticated way than the RW. The result is fewer likelihood evaluations, improved exploration of challenging posterior distributions and an improved ability to perform likelihood evaluations in parallel. Another consequence of using independent proposals is that all candidates generated in the SMC process can be used to estimate the marginal likelihood and posterior expectations. We consider various importance sampling (IS) estimators that use all candidates and devise a novel IS marginal likelihood estimator. 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