A note on auxiliary particle filters

The auxiliary particle filter (APF) introduced by Pitt and Shephard [Pitt, M.K., Shephard, N., 1999. Filtering via simulation: Auxiliary particle filters. J. Am. Statist. Ass. 94, 590–599] is a very popular alternative to Sequential Importance Sampling and Resampling (SISR) algorithms to perform inf...

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Bibliographic Details
Published inStatistics & probability letters Vol. 78; no. 12; pp. 1498 - 1504
Main Authors Johansen, Adam M., Doucet, Arnaud
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.09.2008
Elsevier
SeriesStatistics & Probability Letters
Subjects
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Summary:The auxiliary particle filter (APF) introduced by Pitt and Shephard [Pitt, M.K., Shephard, N., 1999. Filtering via simulation: Auxiliary particle filters. J. Am. Statist. Ass. 94, 590–599] is a very popular alternative to Sequential Importance Sampling and Resampling (SISR) algorithms to perform inference in state-space models. We propose a novel interpretation of the APF as an SISR algorithm. This interpretation allows us to present simple guidelines to ensure good performance of the APF and the first convergence results for this algorithm. Additionally, we show that, contrary to popular belief, the asymptotic variance of APF-based estimators is not always smaller than those of the corresponding SISR estimators — even in the ‘perfect adaptation’ scenario.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2008.01.032