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An EM algorithm for estimation in Markov-modulated Poisson processes. (English) Zbl 0875.62405

Summary: It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. We present an EM algorithm for computing such estimates and discuss how it may be implemented. We also compare it to the Nelder-Mead downhill simplex algorithm for some numerical examples, and the results show that the number of iterations the EM algorithm requires to converge is in general smaller than the number of likelihood evaluations required by the downhill simplex algorithm. An EM iteration is more complicated than a likelihood evaluation, though, and thus also implementation aspects must be taken into account to determine the efficiencies of the algorithms.

MSC:

62M05 Markov processes: estimation; hidden Markov models
65C99 Probabilistic methods, stochastic differential equations
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