A note on auxiliary particle filters

• Published in: Statistics & probability letters Vol. 78; no. 12; pp. 1498 - 1504
• Main Authors: Johansen, Adam M., Doucet, Arnaud
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2008; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Exact sciences and technology; General topics; Inference from stochastic processes; time series analysis; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic processes; Filtering; Variance estimation; Probability theory; State space; Statistical estimation; State space method; Asymptotic variance; Algorithm; Convergence; Statistical method; Simulation; Sequential method; Resampling method; Importance sampling; Physical Sciences
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2008.01.032

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.