Phasic Triplet Markov Chains

Abstract

Abstract-Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

Modeling Repayment Behavior of Consumer Loan in Portfolio across Business Cycle: A Triplet Markov Model Approach

“…e model is called a TMM if there exists a stochastic process , where takes its value in a nite set, such that the triplet ( , , ) is a Markov chain. TMM has been applied in the context of signal processing image processing and others [16][17][18][19]. To the authors' knowledge, there is little research that links credit risk measurement with TMM.…”