May 2024 Variance estimation for sequential Monte Carlo algorithms: A backward sampling approach
Yazid Janati El Idrissi, Sylvain Le Corff, Yohan Petetin
Author Affiliations +
Bernoulli 30(2): 911-935 (May 2024). DOI: 10.3150/23-BEJ1586

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 (Bernoulli 23 (2017) 1951–1996). 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.

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Yazid Janati El Idrissi. Sylvain Le Corff. Yohan Petetin. "Variance estimation for sequential Monte Carlo algorithms: A backward sampling approach." Bernoulli 30 (2) 911 - 935, May 2024. https://doi.org/10.3150/23-BEJ1586

Information

Received: 1 April 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699539
Digital Object Identifier: 10.3150/23-BEJ1586

Keywords: asymptotic variance , central limit theorem , particle filtering , particle smoothing , Sequential Monte Carlo methods

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Vol.30 • No. 2 • May 2024
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