An EM algorithm for the model fitting of Markovian binary trees

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.