Parameter estimation for a discretely observed population process under Markov-modulation

A Markov-modulated independent sojourn process is a population process in which individuals arrive according to a Poisson process with Markov-modulated arrival rate, and leave the system after an exponentially distributed time. A procedure is developed to estimate the parameters of such a system, including those related to the modulation. It is assumed that the number of individuals in the system is observed at equidistant time points only, whereas the modulating Markov chain cannot be observed at all. An algorithm is set up for finding maximum likelihood estimates, based on the EM algorithm and containing a forward–backward procedure for computing the conditional expectations. To illustrate the performance of the algorithm the results of an extensive simulation study are presented.