Johansen, Adam M. and Doucet, Arnaud. (2008) A note on auxiliary particle filters. Statistics & Probability Letters, Vol.78 (No.12). pp. 1498-1504. ISSN 01677152

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Abstract

The Auxiliary Particle Filter (APF) introduced by Pitt and Shephard (1999) 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.

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Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Filters (Mathematics), State-space methods, Inference
Journal or Publication Title:	Statistics & Probability Letters
Publisher:	Elsevier Science BV
ISSN:	01677152
Date:	1 September 2008
Volume:	Vol.78
Number:	No.12
Page Range:	pp. 1498-1504
Identification Number:	10.1016/j.spl.2008.01.032
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
References:	[1] Carpenter, J., Clifford, P. and Fearnhead, P. (1999) An improved particle filter for non-linear problems. IEE proceedings - Radar, Sonar and Navigation, 146, 2-7. [2] Chopin, N. (2004) Central limit theorem for sequential Monte Carlo and its application to Bayesian inference. Ann. Statist., 32, 2385-2411. [3] Del Moral, P. (2004) Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications, Series Probability and Applications, New York: Springer-Verlag. [4] Del Moral, P., Doucet, A. and Peters, G.W. (2007) Sharp propagation of chaos estimates for Feynman-Kac particle models. Theory of Probability and Its Applications 51, 459-485. [5] Doucet, A., Godsill, S.J. and Andrieu, C. (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197- 208. [6] Doucet, A., de Freitas, J.F.G. and Gordon, N.J. (eds.) (2001) Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag. [7] Fearnhead, P., Papaspiliopoulos, O. and Roberts, G.O. (2007) Particle filters for partially-observed diffusions. Technical report, Lancaster University. [8] Godsill, S.J. and Clapp, T. (2001) Improvement strategies for Monte Carlo particle filters, in [6], 139-158. [9] Johansen, A.M. (2006) Some non-standard sequential Monte Carlo methods and their applications. PhD Thesis, Cambridge University. [10] Johansen, A.M. and Doucet, A. (2007) Auxiliary variable sequential Monte Carlo methods. Statistics Group Technical Report, 07:09, University of Bristol. http://www.stats.bris.ac.uk/research/stats/reports/2007/ [11] Liu, J.S. (2001) Monte Carlo Strategies in Scientific Computing. New York: Springer-Verlag. [12] Pitt, M.K. and Shephard, N. (1999). Filtering via simulation: auxiliary particle filters. J. Am. Statist. Ass., 94, 590-599. [13] Pitt, M.K. and Shephard, N. (2001). Auxiliary variable based particle filters, in [6], 271–293.
URI:	http://wrap.warwick.ac.uk/id/eprint/37283

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