Journal of Applied Probability

On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions

Ajay Jasra

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Abstract

We consider the time behaviour associated to the sequential Monte Carlo estimate of the backward interpretation of Feynman-Kac formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models. We prove a central limit theorem under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression for additive functionals grows at most linearly in time under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some hidden Markov models.

Article information

Source
J. Appl. Probab., Volume 52, Number 2 (2015), 339-359.

Dates
First available in Project Euclid: 23 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1437658602

Digital Object Identifier
doi:10.1239/jap/1437658602

Mathematical Reviews number (MathSciNet)
MR3372079

Zentralblatt MATH identifier
1327.62036

Subjects
Primary: 64C05
Secondary: 62F15: Bayesian inference

Keywords
Particle filter central limit theorem smoothing

Citation

Jasra, Ajay. On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions. J. Appl. Probab. 52 (2015), no. 2, 339--359. doi:10.1239/jap/1437658602. https://projecteuclid.org/euclid.jap/1437658602


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