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Nonparametric particle filtering approaches for identification and inference in nonlinear state-space dynamic systems

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Abstract

Most system identification approaches and statistical inference methods rely on the availability of the analytic knowledge of the probability distribution function of the system output variables. In the case of dynamic systems modelled by hidden Markov chains or stochastic nonlinear state-space models, these distributions as well as that of the state variables themselves, can be unknown or untractable. In that situation, the usual particle Monte Carlo filters for system identification or likelihood-based inference and model selection methods have to rely, whenever possible, on some hazardous approximations and are often at risk. This review shows how a recent nonparametric particle filtering approach can be efficiently used in that context, not only for consistent filtering of these systems but also to restore these statistical inference methods, allowing, for example, consistent particle estimation of Bayes factors or the generalisation of model parameter change detection sequential tests.

Real-life applications of these particle approaches to a microbiological growth model are proposed as illustrations.

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Acknowledgements

The authors would like to thank both reviewers for their careful reading of the manuscript, relevant remarks and new references, which helped to improve the quality of the paper.

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Authors and Affiliations

  1. Unité MIA (UR341), INRA Domaine de Vilvert, 78352, Jouy-en-Josas, France

    Jean-Pierre Gauchi

  2. UMR MISTEA, SupAgro-INRA, 2 place P. Viala, 34060, Montpellier, France

    Jean-Pierre Vila

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  1. Jean-Pierre Gauchi
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Correspondence to Jean-Pierre Gauchi.

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Gauchi, JP., Vila, JP. Nonparametric particle filtering approaches for identification and inference in nonlinear state-space dynamic systems. Stat Comput 23, 523–533 (2013). https://doi.org/10.1007/s11222-012-9327-7

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