Abstract
Sequential Monte Carlo (SMC) samplers are an alternative to MCMC for Bayesian computation. However, their performance depends strongly on the Markov kernels used to rejuvenate particles. We discuss how to calibrate automatically (using the current particles) Hamiltonian Monte Carlo kernels within SMC. To do so, we build upon the adaptive SMC approach of Fearnhead and Taylor (2013), and we also suggest alternative methods. We illustrate the advantages of using HMC kernels within an SMC sampler via an extensive numerical study.
Highlights
Sequential Monte Carlo (SMC) samplers (Neal, 2001; Chopin, 2002; Del Moral et al, 2006) approximate a target distribution π by sampling particles from an initial distribution π0, and moving them through a sequence of distributions πt which ends at πT = π
The main contribution of this paper is to investigate this tuning in the case of Hamiltonian Monte Carlo (HMC) kernels, and is described in Section 3. (a) Choice of the exponent A common approach (Jasra et al, 2011; Schafer and Chopin, 2013) to choose adaptively intermediate distributions within SMC is to rely on the ESS
In order to assess the performance of the two tuning procedures (FT and PR), we compare the tuning parameters obtained at the final stage of our SMC samplers (HMCAFT and HMCAPR) with those obtained from the following Markov chain Monte Carlo (MCMC) procedures: NUTS (Hoffman and Gelman, 2014) and the adaptive MCMC algorithm of Mohamed et al (2013)
Summary
In Bayesian computation this approach has several advantages over Markov chain Monte Carlo (MCMC). It enables the estimation of normalizing constants and can be used for model choice (Zhou et al, 2016). The propagation of the particles commonly relies on MCMC kernels, which depend on some tuning parameters. Choosing these parameters in a sensible manner is challenging and is of interest both from a theoretical and practical point of view; see Fearnhead and Taylor (2013); Schafer and Chopin (2013); Beskos et al (2016).
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