represents a powerful alternative to methods for sampling from the posterior distribution of static Bayesian models. SMC involves specifying a sequence of distributions connecting one that is easy to sample from with one that is the target, the posterior distribution. SMC uses a sequence of reweighting, resampling and move steps to traverse a population of particles through this sequence of distributions. The move step is important as it is generally the most computationally expensive step and is critical in maintaining particle diversity. A common choice in the literature is to adopt an MCMC kernel for the move step, which can utilise the population of particles to help devise efficient proposals. Since the MCMC kernel may reject proposals, the kernel may be applied a fixed prescribed number of times on each particle. In this paper we propose to take further advantage of the population of particles by forming an independent proposal based on a copula model. An interesting by-product of the independent proposal choice is that we are able to consider various importance sampling (IS) estimators of the marginal likelihood or the evidence. We devise a novel IS evidence estimator and compare it with other IS-based estimators and the standard SMC estimator. We demonstrate on several examples in this paper that our novel approach with independent proposals can lead to more efficient posterior approximations and more accurate estimates of the evidence compared with other derivative-free MCMC proposals.
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