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

Julien Cornebise; Eric Moulines; Jimmy Olsson

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arXiv · 0803.0054

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

Julien Cornebise·Eric Moulines·Jimmy Olsson

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Abstract

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.

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Julien Cornebise, Eric Moulines, Jimmy Olsson. 2008-08-23. Adaptive methods for sequential importance sampling with application to state space models. https://arxiv.org/abs/0803.0054

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