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On the Behaviour of the Backward Interpretation of Feynman-Kac Formulae Under Verifiable Conditions

Part of: Parametric inference

Published online by Cambridge University Press:  30 January 2018

Ajay Jasra
Ajay Jasra*
Affiliation:
National University of Singapore
*
∗ Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, 117546, Singapore. Email address: staja@nus.edu.sg
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Abstract

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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.

Keywords

Particle filtercentral limit theoremsmoothing

MSC classification

Secondary: 62F15: Bayesian inference
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 339 - 359
Copyright
© Applied Probability Trust 

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