A general theory of particle filters in hidden Markov models and some applications

Abstract

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.

Published in at http://dx.doi.org/10.1214/13-AOS1172 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Recursive Monte Carlo filters: Algorithms and theoretical analysis
• Sequentially interacting Markov chain Monte Carlo methods
• A sequential Monte Carlo approach to computing tail probabilities in stochastic models

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