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

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

Research output: Contribution to JournalArticleAcademicpeer-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 languageEnglish
Pages (from-to)88-103
Number of pages16
JournalComputational Statistics and Data Analysis
Volume140
Early online date26 Jun 2019
DOIs
Publication statusE-pub ahead of print - 26 Jun 2019

Fingerprint

Parameter estimation
Parameter Estimation
Modulation
Equidistant
Conditional Expectation
EM Algorithm
Maximum Likelihood Estimate
Poisson process
Markov processes
Maximum likelihood
Markov chain
Simulation Study
Computing
Estimate

Keywords

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

Cite this

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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.",
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Parameter estimation for a discretely observed population process under Markov-modulation. / de Gunst, Mathisca; Knapik, Bartek; Mandjes, Michel; Sollie, Birgit.

In: Computational Statistics and Data Analysis, Vol. 140, 12.2019, p. 88-103.

Research output: Contribution to JournalArticleAcademicpeer-review

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

AU - de Gunst, Mathisca

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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.

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KW - Infinite server queue

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KW - Population process

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