On the complexity of standard and waste-free SMC samplers

TL;DR

This paper derives finite sample bounds for standard and waste-free SMC samplers, analyzing their error in estimating expectations and normalising constants, and provides practical implementation guidance.

Contribution

It establishes theoretical error bounds for SMC samplers across different scenarios, including arbitrary and tempering sequences, and discusses their complexity and practical use.

Findings

Finite sample bounds for SMC error estimates.

Complexity analysis with respect to number of distributions and dimension.

Practical recommendations for SMC implementation.

Abstract

We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of distributions, and then specialise our results to tempering sequences. We use our results to derive the complexity of SMC samplers with respect to the parameters of the problem, such as $T$, the number of target distributions, in the general case, or $d$, the dimension of the ambient space, in the tempering case. We use these bounds to derive practical recommendations for the implementation of SMC samplers for end users.