OPTIMALITY OF THE AUXILIARY PARTICLE FILTER
Randal Douc
Éric Moulines
Jimmy Olsson
Abstract: 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 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.
2000 AMS Mathematics Subject Classification: Primary: 65C05; Secondary:
65C60.
Keywords and phrases: Auxiliary particle filter, central limit theorem, adjustment
multiplier weight, sequential Monte Carlo, state space model, stratified sampling, two-stage
sampling.