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

Abstract. In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms--also known as particle filters--relying on new criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is of 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 byproduct of this analysis we obtain an adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish and justify an entropy criterion of linear complexity which can used for estimating 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 resul...

• Type: Journal
• Year: 2008
• Where: SAC
• Authors: Julien Cornebise, Eric Moulines, Jimmy Olsson
• Keywords: Applied Computing, Auxiliary Particle Filter, Monte Carlo, SAC 2008, Sequential Monte Carlo