Statistical analysis on Markov-modulated Poisson processes

A class of doubly stochastic Poisson processes, which is termed a Markov-modulated Poisson process, is studied. The maximum likelihood method is used to make inferences about the Markov-modulated Poisson process. Expressions are derived for the likelihood function and for second-order properties of both counts and intervals. A simple two-state model is applied to a set of exposure data and to simulated data. Bivariate generalization of this process is also studied