Particle approximations of the score and observed information matrix in state space models with application to parameter estimation

Particle methods are popular computational tools for Bayesian inference in nonlinear non-Gaussian state space models. For this class of models, we present two particle algorithms to compute the score vector and observed information matrix recursively. The first algorithm is implemented with computat...

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Bibliographic Details
Published inBiometrika Vol. 98; no. 1; pp. 65 - 80
Main Authors Doucet, Arnaud, Poyiadjis, George, Singh, Sumeetpal S
Format Journal Article
LanguageEnglish
Published Oxford University Press for Biometrika Trust 01.03.2011
SeriesBiometrika
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Summary:Particle methods are popular computational tools for Bayesian inference in nonlinear non-Gaussian state space models. For this class of models, we present two particle algorithms to compute the score vector and observed information matrix recursively. The first algorithm is implemented with computational complexity and the second with complexity , where N is the number of particles. Although cheaper, the performance of the  method degrades quickly, as it relies on the approximation of a sequence of probability distributions whose dimension increases linearly with time. In particular, even under strong mixing assumptions, the variance of the estimates computed with the  method increases at least quadratically in time. The more expensive  method relies on a nonstandard particle implementation and does not suffer from this rapid degradation. It is shown how both methods can be used to perform batch and recursive parameter estimation. Copyright 2011, Oxford University Press.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asq062