Properties of marginal sequential Monte Carlo

Francesca Crucinio; Adam M. Johansen

doi:10.1016/j.spl.2023.109914

Properties of marginal sequential Monte Carlo

Francesca Crucinio, Adam M. Johansen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a framework which admits a number of "marginal" sequential Monte Carlo (SMC) algorithms as particular cases - including the marginal particle filter (Klaas et al., 2005), the independent particle filter (Lin et al., 2005) and linear-cost Approximate Bayesian Computation SMC (Sisson et al., 2007). We provide conditions under which such algorithms obey laws of large numbers and central limit theorems and provide some further asymptotic characterizations. Finally, it is shown that the asymptotic variance of a class of estimators associated with certain marginal SMC algorithms is never greater than that of the estimators provided by a standard SMC algorithm using the same proposal distributions.

Original language	English
Journal	Statistics & Probability Letters
Volume	203
DOIs	https://doi.org/10.1016/j.spl.2023.109914
Publication status	Published - 1 Dec 2023

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10.1016/j.spl.2023.109914

https://doi.org/10.1016/j.spl.2023.109914

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AU - Johansen, Adam M.

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N2 - We provide a framework which admits a number of "marginal" sequential Monte Carlo (SMC) algorithms as particular cases - including the marginal particle filter (Klaas et al., 2005), the independent particle filter (Lin et al., 2005) and linear-cost Approximate Bayesian Computation SMC (Sisson et al., 2007). We provide conditions under which such algorithms obey laws of large numbers and central limit theorems and provide some further asymptotic characterizations. Finally, it is shown that the asymptotic variance of a class of estimators associated with certain marginal SMC algorithms is never greater than that of the estimators provided by a standard SMC algorithm using the same proposal distributions.

AB - We provide a framework which admits a number of "marginal" sequential Monte Carlo (SMC) algorithms as particular cases - including the marginal particle filter (Klaas et al., 2005), the independent particle filter (Lin et al., 2005) and linear-cost Approximate Bayesian Computation SMC (Sisson et al., 2007). We provide conditions under which such algorithms obey laws of large numbers and central limit theorems and provide some further asymptotic characterizations. Finally, it is shown that the asymptotic variance of a class of estimators associated with certain marginal SMC algorithms is never greater than that of the estimators provided by a standard SMC algorithm using the same proposal distributions.

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DO - 10.1016/j.spl.2023.109914

M3 - Article

SN - 0167-7152

VL - 203

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

ER -

Properties of marginal sequential Monte Carlo

Abstract

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