Models Comparison
Irene Votsi, Nikolaos Limnios, Eleftheria E. Papadimitriou, George M. Tsaklidis · 2018
Markov chains are the simplest stochastic models that can be used to describe time-varying, random phenomena. This chapter presents the comparison of hidden Markov models (HMMs) and hidden Markov renewal models (HMRMs) in a Markov context and a Markov renewal context, and determines whether there are any differences in terms of their transition probability matrices. It explores the framework within which the application of HMMs is satisfactory or the application of more complex HMRMs can be justified. The chapter describes the Monte Carlo algorithm. The Baum-Welch algorithm converges when the absolute log-likelihood converges. The complexity characterizing HMRMs can be justified in a semi-Markov framework, since the total variation distance between the estimator and the "true" value of the parameter is smaller than the respective value of an HMM. On the contrary, in a Markov context, both HMMs and HMRMs lead to a good description of the corresponding observations.