Waste-free sequential Monte Carlo

A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems).

Automated summary

The paper proposes a new waste-free sequential Monte Carlo (SMC) algorithm that utilizes the outputs of all intermediate Markov chain Monte Carlo (MCMC) steps as particles. The consistency and asymptotic normality of its output are established, and insights on estimating the asymptotic variance of any particle estimate are developed. Empirical results show that waste-free SMC tends to outperform standard SMC samplers, particularly in scenarios where the mixing of the considered MCMC kernels decreases across iterations.