Unified Representation of Sets of Heterogeneous Markov Transition Matrices

Markov chains are very efficient models and have been extensively applied in a wide range of fields covering queuing theory, signal processing, performance evaluation, time series, and finance. For discrete finite first-order Markov chains, which are among the most used models of this family, the transition matrix can be seen as the model parameter, since it encompasses the set of probabilities governing the system state. Estimating such a matrix is, however, not an easy task due to possible opposing expert reports or variability of conditions under which the estimation process is carried out. In this paper, we propose an original approach to infer a consensus transition matrix, defined in accordance with the theory of evidence, from a family of data samples or transition matrices. To validate our method, experiments are conducted on nonstationary label images and daily rainfall data. The obtained results confirm the interest of the proposed evidential modeling with respect to the standard Bayesian one.