Increasing the efficiency of Sequential Monte Carlo samplers through the use of approximately optimal L-kernels

Abstract

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, the tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in several ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter – the ‘L-kernel’ – is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid the implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimal L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65% and 70%. Python code and code tests accompanying this manuscript are available through the Github repository https://github.com/plgreenLIRU/SMC_approx_optL.