Properties of marginal sequential Monte Carlo methods

Francesca R. Crucinio; Adam M. Johansen

doi:10.1016/j.spl.2023.109914

Properties of marginal sequential Monte Carlo methods

Francesca R. Crucinio
, Adam M. Johansen

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
Article number	109914
Journal	Statistics and Probability Letters
Volume	203
DOIs	https://doi.org/10.1016/j.spl.2023.109914
Publication status	Published - 1 Dec 2023
Externally published	Yes

Keywords

Asymptotic variance
Central limit theorem
Law of large numbers
Particle filters

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10.1016/j.spl.2023.109914

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title = "Properties of marginal sequential Monte Carlo methods",

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.",

keywords = "Asymptotic variance, Central limit theorem, Law of large numbers, Particle filters",

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AU - Crucinio, Francesca R.

AU - Johansen, Adam M.

PY - 2023/12/1

Y1 - 2023/12/1

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.

KW - Asymptotic variance

KW - Central limit theorem

KW - Law of large numbers

KW - Particle filters

UR - https://www.scopus.com/pages/publications/85168846517

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DO - 10.1016/j.spl.2023.109914

M3 - Article

AN - SCOPUS:85168846517

SN - 0167-7152

VL - 203

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109914

ER -

Properties of marginal sequential Monte Carlo methods

Abstract

Keywords

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