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,
2008
ISSN 14039338

Abstract:

In this paper we discuss new adaptive proposal strategies for sequential
Monte Carlo algorithmsalso known as particle filtersrelying 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 longused coefficient of variation
suggested by Kong et al. (1994) of the weights can be used for estimating
the chisquare distance between the target and instrumental distributions
of the auxiliary particle filter. As

a byproduct of this analysis we obtain an auxiliary adjustment multiplier
weight type for which this chisquare distance is minimal. Moreover, we establish
an empirical estimate of linear complexity of the KullbackLeibler 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.




