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Theory of segmented particle filters

Part of: Parametric inference

Published online by Cambridge University Press:  24 March 2016

Hock Peng Chan ,
Chiang-Wee Heng  and
Ajay Jasra
Hock Peng Chan*
Affiliation:
National University of Singapore
Chiang-Wee Heng*
Affiliation:
National University of Singapore
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.
* Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, 117546, Singapore.
* Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, 117546, Singapore.
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Abstract

We study the asymptotic behavior of a new particle filter approach for the estimation of hidden Markov models. In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall-clock computational time. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. We show that the likelihood function estimator is unbiased, and show asymptotic normality of the underlying estimators.

Keywords

CLTparallel processingSMCstandard error estimation

MSC classification

Secondary: 62F15: Bayesian inference
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 1 , March 2016 , pp. 69 - 87
Copyright
Copyright © Applied Probability Trust 2016 

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