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arXiv · 0709.3448

On the auxiliary particle filter

Randal Douc·Eric Moulines·Jimmy Olsson
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Abstract

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the Lp 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.

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Randal Douc, Eric Moulines, Jimmy Olsson. 2007-09-21. On the auxiliary particle filter. https://arxiv.org/abs/0709.3448

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