Optimal model for a set of Markov processes
Jesús Enrique García, Sergio Luis Mercado Londoño · AIP conference proceedings · 2019
In this paper we develop a model selection procedure for the joint modeling of multiple Markov processes over the same finite alphabet A. The methodology is based on the Bayesian Information Criterion (BIC) by Schwarz [5]. The procedure consists on finding the values on the state space of two or more processes sharing the same transition probabilities. This identification allows us to build a partition of the set of state spaces, such that two states are in the same part if and only if they have the same transition probabilities. Formulating the joint model in this way, the number of parameters is minimized since for each part we need (|A| − 1) parameters. The joint model developed here is a generalization of the partition Markov models by García and González-López [1], [2], [3] and [4].