Sequential Monte Carlo samplers: error bounds and insensitivity to initial conditions

TL;DR

This paper investigates the stability and error bounds of sequential Monte Carlo methods, demonstrating that initial condition effects diminish exponentially with more steps and errors remain stable under certain assumptions.

Contribution

It provides new theoretical results on the stability and error bounds of SMC algorithms, especially regarding insensitivity to initial distributions in non-compact spaces.

Findings

Initial distribution effects decay exponentially with steps

Stochastic error remains stable in _{p} norm

Results applicable to fixed start and end distributions in SMC

Abstract

This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end distributions in the sequence are fixed and the number of intermediate steps is a parameter of the algorithm. Under assumptions which hold on non-compact spaces, it is shown that the effect of the initial distribution decays exponentially fast in the number of intermediate steps and the corresponding stochastic error is stable in \mathbb{L}_{p} norm.