Persistent Sampling: Enhancing the Efficiency of Sequential Monte Carlo

TL;DR

Persistent sampling (PS) enhances Sequential Monte Carlo by reusing particles across iterations, reducing computational costs and improving accuracy in Bayesian inference without extra likelihood evaluations.

Contribution

We introduce persistent sampling, a novel extension of SMC that reuses particles from all previous steps to improve efficiency and accuracy in Bayesian inference.

Findings

PS reduces mean squared error in posterior estimates.

PS achieves lower variance in marginal likelihood estimates.

PS outperforms standard SMC and variants in high-dimensional problems.

Abstract

Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an extension of SMC that systematically retains and reuses particles from all prior iterations to construct a growing, weighted ensemble. By leveraging multiple importance sampling and resampling from a mixture of historical distributions, PS mitigates the need for excessively large particle counts, directly addressing key limitations of SMC such as particle impoverishment and mode collapse. Crucially, PS achieves this without additional likelihood evaluations-weights for persistent particles are computed using cached likelihood values. This framework not only yields more accurate posterior approximations but also produces marginal likelihood estimates with significantly lower variance, enhancing reliability in model comparison. Furthermore, the persistent ensemble enables efficient adaptation of transition kernels by leveraging a larger, decorrelated particle pool. Experiments on high-dimensional Gaussian mixtures, hierarchical models, and non-convex targets demonstrate that PS consistently outperforms standard SMC and related variants, including recycled and waste-free SMC, achieving substantial reductions in mean squared error for posterior expectations and evidence estimates, all at reduced computational cost. PS thus establishes itself as a robust, scalable, and efficient alternative for complex Bayesian inference tasks.