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A coupled Hidden Markov Model (cHMM) is a hidden Markov model whose hidden Markov chain is bi-dimensional. In this paper, we focus to solve the likelihood and the decoding problems of a cHMM whose state space is composed of a continuous part and a discrete part. We adapt Forward, Backward and Viterbi algorithms to be able to study such cHMMs problems. Basic numerical examples are considered to show the well functioning of the elaborated algorithms for our proposal.
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Kroumbi et al. (2025) studied this question.
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