Copulas selection in pairwise Markov chain

The Hidden Markov Chain (HMC) model considers that the process of unobservable states is a Markov chain. The Pairwise Markov Chain (PMC) model however considers the couple of processes of observations and states as a Markov chain. It has been shown that the PMC model is strictly more general than the HMC one, but retains the ease of processings that made the success of HMC in a number of applications. In this work, we are interested in the modeling of class-conditional densities appearing in PMC by bi-dimensional copulas and the mixtures estimation problem. We study the influence of copula shapes on PMC data and the automatic identification of the right copulas from a finite set of admissible copulas, by extending the general “Iterative Conditional Estimation” parameters estimation method to the context considered. A set of systematic experiments conducted with eight families of one-parameters copulas parameterized with Kendall’s tau is proposed. In particular, experiments show that the use of false copulas can degrade significantly classification performances.