RECURSIVE ESTIMATION OF PARAMETERS IN MARKOV-MODULATED POISSON PROCESSES

A hidden Markov regime is a Markov process that governs the time or sp ace dependent distributions of an observed stochastic process. Recursi ve algorithms can be used to estimate parameters in mixed distribution s governed by a Markov regime. Here we derive a recursive algorithm fo r estimation of parameters in a Markov-modulated Poisson process also called a Cox point process. By this we mean a doubly stochastic Poisso n process with a time dependent intensity that can take on a finite nu mber of different values. The intensity switches randomly between the possible values according to a Markov process. We consider two differe nt ways to observe the Markov-modulated Poisson process: in the first model the observations consist of the observed time intervals between events, and in the second model we use the total number of events in s uccessive intervals of fixed length. We derive an algorithm for recurs ive estimation of the Poisson intensities and the switch intensities b etween the two states and illustrate the algorithm in a simulation stu dy. The estimates of the switch intensities are based on the observed conditional switch probabilities.