We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

翻译：我们构建了一个由持续时间马可夫人口过程引发的基因学价值的马可夫过程的组合。我们根据人口过程的历史,得出特定基因学可能性的确切表达方式。这导致一个非线性过滤方程式,可用于设计高效的蒙特卡洛推理算法。我们用几个例子来证明这些计算。现有的关于植物动力学推理的完整信息方法是理论的特殊例子。