Hautphenne Sophie, Massaro Melanie, Taylor Peter
School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia.
Institute of Mathematics, Ecole polytechnique fédérale de Lausanne, Lausanne, Vaud, Switzerland.
J Math Biol. 2017 Dec;75(6-7):1319-1347. doi: 10.1007/s00285-017-1121-x. Epub 2017 Apr 3.
In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.
在本文中，我们使用一个具有一个吸收态的有限状态连续时间马尔可夫链来对个体的寿命进行建模。在这个模型下，死亡时间服从相位型分布，并且马尔可夫链的瞬态状态被称为阶段。然后，我们试图回答一个简单的问题：“给定个体当前所处阶段，其条件年龄分布是什么？”我们表明，答案取决于我们如何解释这个问题，特别是取决于所考虑的阶段观测方案。接着，我们将我们的结果应用于计算2007 - 2014年监测期间濒危的查塔姆岛黑知更鸟（Petroica traversi）的年龄金字塔。
