Optimality of the auxiliary particle filter

• Autorzy: Douc R. , Moulines É , Olsson J.
• Języki publikacji: EN

Abstrakty

EN

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard [17]. Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the L^p error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance of the CLT we identify first-stage importance weights for which the increase of asymptotic variance at a single iteration of the algorithm is minimal. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.

Słowa kluczowe

EN

auxiliary particle filter; central limit theorem; adjustment multiplier weight; sequential Monte Carlo; state space model; stratified sampling; two stage sampling

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2009
• Tom: Vol. 29, Fasc. 1
• Strony: 1--28
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Douc R.

• Département CITI, Télécom SudParis, 9 Rue Charles Fourier, 91011 Evry Cedex, France

autor

Moulines É

• Département TSI, Institut des Télécoms, Télécom ParisTech, 46 Rue Barrault, 75634 Paris Cedex 13, France

autor

Olsson J.

• Center of Mathematical Sciences, Lund University, Box 118, SE-22100, Lund, Sweden

Bibliografia

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