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

Mathisca de Gunst; Bartek Knapik; Michel Mandjes; Birgit Sollie

doi:10.1016/j.csda.2019.06.008

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 Journal › Article › Academic › peer-review

Abstract

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 language	English
Pages (from-to)	88-103
Number of pages	16
Journal	Computational Statistics and Data Analysis
Volume	140
Early online date	26 Jun 2019
DOIs	https://doi.org/10.1016/j.csda.2019.06.008
Publication status	Published - Dec 2019

Funding

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

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	024002003

Keywords

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

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10.1016/j.csda.2019.06.008

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title = "Parameter estimation for a discretely observed population process under Markov-modulation",

abstract = "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.",

keywords = "EM algorithm, Infinite server queue, Markov modulation, Maximum likelihood estimation, Population process",

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year = "2019",

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doi = "10.1016/j.csda.2019.06.008",

language = "English",

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T1 - Parameter estimation for a discretely observed population process under Markov-modulation

AU - de Gunst, Mathisca

AU - Knapik, Bartek

AU - Mandjes, Michel

AU - Sollie, Birgit

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

KW - EM algorithm

KW - Infinite server queue

KW - Markov modulation

KW - Maximum likelihood estimation

KW - Population process

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JO - Computational Statistics and Data Analysis

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ER -

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

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Keywords

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