Parameter estimation for a discretely observed population process under Markov-modulation

Mathisca de Gunst, Bartek Knapik, Michel Mandjes, Birgit Sollie*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


A Markov-modulated independent sojourn process is a population process in which individuals arrive according to a Poisson process with Markov-modulated arrival rate, and leave the system after an exponentially distributed time. A procedure is developed to estimate the parameters of such a system, including those related to the modulation. It is assumed that the number of individuals in the system is observed at equidistant time points only, whereas the modulating Markov chain cannot be observed at all. An algorithm is set up for finding maximum likelihood estimates, based on the EM algorithm and containing a forward–backward procedure for computing the conditional expectations. To illustrate the performance of the algorithm the results of an extensive simulation study are presented.

Original languageEnglish
Pages (from-to)88-103
Number of pages16
JournalComputational Statistics and Data Analysis
Early online date26 Jun 2019
Publication statusPublished - Dec 2019


MM was supported by the NWO Gravitation program NETWORKS, grant 024002003 .

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek024002003


    • EM algorithm
    • Infinite server queue
    • Markov modulation
    • Maximum likelihood estimation
    • Population process


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