Estimation in the Mixture of Markov Chains

Abstract

This paper considers a new mixture of time homogeneous finite Markov chains where the mixing is on the rate of movement and develops the EM algorithm for the maximum likelihood estimation of the parameters of the mixture. A continuous and discrete time versions of the mixture are defined and their estimation is considered separately. The simulation study is carried out for the continuous time mixture. To simplify the exposition the results are derived for a mixture of two Markov chains, but can be easily extended to a mixture of any finite number of Markov chains. The class of mixture models proposed in this paper provides a framework for modeling population heterogeneity with respect to the rate of movement. The proposed mixture generalizes the mover-stayer model, which has been widely employed in applications.