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Statistical inference for discretely observed Markov jump processes

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Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator does not exist, an estimator can be obtained by using a penalized likelihood function or by the Markov chain Monte Carlo procedure with a suitable prior. The methodology and its implementation are illustrated by examples and simulation studies.

Keywords: EM algorithm; Imbedding problem; Likelihood inference; Markov chain Monte Carlo methods

Document Type: Research Article


Affiliations: 1: Universidad Nacional Autónoma de México, México 2: University of Copenhagen, Denmark

Publication date: June 1, 2005


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