Non-asymptotic Error Bounds for Sequential MCMC and Stability of Feynman-Kac Propagators

TL;DR

This paper develops a framework for deriving non-asymptotic error bounds for Sequential MCMC methods by linking stability of Feynman-Kac propagators to mixing conditions and density bounds.

Contribution

It introduces a generic approach to obtain error bounds for Sequential MCMC based on stability properties derived from mixing conditions and density bounds.

Findings

Non-asymptotic error bounds are established for Sequential MCMC.

Stability of Feynman-Kac propagators can be derived from spectral gaps and hyperboundedness.

The method connects mixing conditions to error control in Sequential MCMC.

Abstract

We provide a generic way of deducing non-asymptotic error bounds for Sequential MCMC methods from suitable stability properties of Feynman-Kac propagators. We show how to derive this type of stability from mixing conditions for the MCMC dynamics, namely, spectral gaps and hyperboundedness, and from upper bounds on the relative densities in the sequence of distributions.