Sequential Monte Carlo smoothing for general state space hidden Markov models

Details Sequential Monte Carlo smoothing for general state space hidden Markov models Sequential Monte Carlo smoothing for general state space hidden Markov models

2012-02-14

arxiv.org/abs/1202.2945v1

Annals of Applied Probability 2011, Vol. 21, No. 6, 2109-2145

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP735 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP735

Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles.

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