Adaptive methods for sequential importance sampling with application to state space models

Julien Cornebise, Èric Moulines and Jimmy Olsson

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms---also known as particle filters---relying on criterions evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation suggested by Kong et al. (1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As
a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution, e.g., by means of population Monte Carlo techniques, and illustrate the methods on several numerical examples.