Adaptive methods for sequential importance sampling with application to state space models |
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Authors: | Julien Cornebise Éric Moulines Jimmy Olsson |
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Institution: | (1) Institut des Télécoms, Télécom ParisTech, 46 Rue Barrault, 75634 Paris Cedex 13, France;(2) Center of Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden |
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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 (suggested
by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 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 and illustrate the methods on a numerical example.
This work was partly supported by the National Research Agency (ANR) under the program “ANR-05-BLAN-0299”. |
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Keywords: | Adaptive Monte Carlo Auxiliary particle filter Coefficient of variation Kullback-Leibler divergence Cross-entropy method Sequential Monte Carlo State space models |
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