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Fitting Markovian binary trees using global and individual demographic data

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  • Hautphenne, Sophie
  • Massaro, Melanie
  • Turner, Katharine

Abstract

We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:128:y:2019:i:c:p:39-50
    DOI: 10.1016/j.tpb.2019.04.007
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    References listed on IDEAS

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    1. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    2. Paraskevi Peristera & Anastasia Kostaki, 2007. "Modeling fertility in modern populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 16(6), pages 141-194.
    3. 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.
    4. Sophie Hautphenne & Guy Latouche & Marie-Ange Remiche, 2011. "Algorithmic Approach to the Extinction Probability of Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 171-192, March.
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