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An EM algorithm for the model fitting of Markovian binary trees

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  • Hautphenne, Sophie
  • Fackrell, Mark

Abstract

Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation–Maximization (EM) algorithm is developed to estimate the parameters of the Markov process from the continuous observation of some populations, first with information about which individuals reproduce or die (the distinguishable case), and second without this information (the indistinguishable case). The performance of the EM algorithm is illustrated with some numerical examples. Fits resulting from the distinguishable case are shown not to be significantly better than fits resulting from the indistinguishable case using some goodness of fit measures.

Suggested Citation

  • Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:19-34
    DOI: 10.1016/j.csda.2013.08.015
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    References listed on IDEAS

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    1. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
    2. Lothar Breuer, 2002. "An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure," Annals of Operations Research, Springer, vol. 112(1), pages 123-138, April.
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    Cited by:

    1. Nina Daskalova, 2017. "Expectation maximization estimates of the offspring probabilities in a class of multitype branching processes with binary family trees," Mathematical Population Studies, Taylor & Francis Journals, vol. 24(4), pages 246-256, October.
    2. Hautphenne, Sophie & Massaro, Melanie & Turner, Katharine, 2019. "Fitting Markovian binary trees using global and individual demographic data," Theoretical Population Biology, Elsevier, vol. 128(C), pages 39-50.
    3. González, M. & Minuesa, C. & del Puerto, I., 2016. "Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 209-227.

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