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

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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.

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Authors and Affiliations

  1. Institut des Télécoms, Télécom ParisTech, 46 Rue Barrault, 75634, Paris Cedex 13, France

    Julien Cornebise & Éric Moulines

  2. Center of Mathematical Sciences, Lund University, Box 118, SE-22100, Lund, Sweden

    Jimmy Olsson

Authors
  1. Julien Cornebise
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  2. Éric Moulines
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  3. Jimmy Olsson
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Correspondence to Julien Cornebise.

Additional information

This work was partly supported by the National Research Agency (ANR) under the program “ANR-05-BLAN-0299”.

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Cornebise, J., Moulines, É. & Olsson, J. Adaptive methods for sequential importance sampling with application to state space models. Stat Comput 18, 461–480 (2008). https://doi.org/10.1007/s11222-008-9089-4

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