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On some extensions of the sequential Monte Carlo methods in high-order hidden Markov models. (English. French summary) Zbl 1420.60095
Summary: We analyze some extensions of the Sequential Monte Carlo (SMC) methods in the context of nonlinear state space models. Namely, we tailor the SMC methods to handle high-order HMM through the customary recursions of posterior distributions. It proceeds on mimicking the two-step procedure that is, the prediction step and the update step, in the derivation of the filter distribution. Once stated, we extend some smoothing recursions as the Forward-Backward algorithm and the Backward smoother to deal with the actual smoothing distributions in high-order HMM. Finally, we give few examples as an application of these extensions.
MSC:
60J05 Discrete-time Markov processes on general state spaces
62M05 Markov processes: estimation; hidden Markov models
65C05 Monte Carlo methods
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