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

Julien Cornebise (1) , Eric Moulines (1) , Jimmy Olsson (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 CMS - Center for Mathematical Sciences

In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms---also known as particle filters---relying on criteria 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 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 and illustrate the methods on a numerical example.

Mots clés: Adaptive Monte Carlo; Auxiliary particle filter; Coefficient of variation; Kullback-Leibler divergence; Cross-entropy method; Sequential Monte Carlo; State space models

Domaines: Calcul [stat.CO]; Statistiques [math.ST]; Théorie [stat.TH]; Méthodologie [stat.ME]

Julien Cornebise, Eric Moulines, Jimmy Olsson. Adaptive methods for sequential importance sampling with application to state space models. 2008. ⟨hal-00259951v2⟩