Variance estimation for Sequential Monte Carlo Algorithms: a backward sampling approach

TL;DR

This paper introduces a new backward sampling-based estimator for online asymptotic variance in particle filtering and smoothing, offering improved stability and reduced variance compared to existing methods.

Contribution

It proposes a novel variance estimator using backward weights, addressing instability and tuning issues of current solutions, and enhances computational efficiency with a PaRIS-inspired approach.

Findings

The new estimator is weakly consistent.

It improves stability and reduces variance in particle filtering.

An efficient estimator for particle smoothing is developed.

Abstract

In this paper, we consider the problem of online asymptotic variance estimation for particle filtering and smoothing. Current solutions for the particle filter rely on the particle genealogy and are either unstable or hard to tune in practice. We propose to mitigate these limitations by introducing a new estimator of the asymptotic variance based on the so called backward weights. The resulting estimator is weakly consistent and trades computational cost for more stability and reduced variance. We also propose a more computationally efficient estimator inspired by the PaRIS algorithm of Olsson & Westerborn. As an application, particle smoothing is considered and an estimator of the asymptotic variance of the Forward Filtering Backward Smoothing estimator applied to additive functionals is provided.