We consider genealogies arising from a Markov population process in which individuals are categorized into a discrete collection of compartments, with the requirement that individuals within the same compartment are statistically exchangeable. When equipped with a sampling process, each such population process induces a time-evolving tree-valued process defined as the genealogy of all sampled individuals. We provide a construction of this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of filter equations. These filter equations can be numerically solved using standard Monte Carlo integration methods. Thus, we obtain statistically efficient likelihood-based inference for essentially arbitrary compartment models based on an observed genealogy of individuals sampled from the population.

翻译：我们研究由马尔可夫群体过程产生的谱系，其中个体被划分为离散的区室集合，并要求同一区室内的个体在统计上可交换。当配备抽样过程时，每个此类群体过程会导出一个时变的树值过程，该过程定义为所有抽样个体的谱系。我们给出了该谱系过程的构造方法，并基于滤波方程推导出观测谱系似然的精确表达式。这些滤波方程可通过标准蒙特卡洛积分方法进行数值求解。由此，我们能够基于从群体中抽样的个体观测谱系，对本质上任意的区室模型实现统计高效的基于似然的推断。