MPS-RR 2003-21
September 2003

Statistical Inference for Discretely Observed Markov Jump Processes

Abstract

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 embedding 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 MCMC-procedure with a suitable prior. The theory is illustrated by a simulation study.

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This paper has now been published in Journal of the Royal Statistical Society, Ser. B. (to appear)