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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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
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
Online AccessGet full text

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Abstract 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.
AbstractList 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 APFÂ as an SISRÂ 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.
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.
Author Doucet, Arnaud
Johansen, Adam M.
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  givenname: Arnaud
  surname: Doucet
  fullname: Doucet, Arnaud
  email: arnaud@stat.ubc.ca
  organization: Departments of Statistics & Computer Science, University of British Columbia, Vancouver, BC, Canada
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10.1111/j.1467-9868.2008.00661.x
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10.1023/A:1008935410038
10.2307/2670179
10.1049/ip-rsn:19990255
10.1214/009053604000000698
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Issue 12
Keywords 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
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Snippet The auxiliary particle filter (APF) introduced by Pitt and Shephard [Pitt, M.K., Shephard, N., 1999. Filtering via simulation: Auxiliary particle filters. J....
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SubjectTerms 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
Title A note on auxiliary particle filters
URI https://dx.doi.org/10.1016/j.spl.2008.01.032
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