Likelihood and decoding problems for mixed space hidden Markov model

Abstract

Abstract A Hidden Markov Model (HMM) is a couple of stochastic processes: A hidden Markov process and an observed emission process. Generally, the HMMs are used to study the hidden behavior of random systems through some observed emission sequences generated by the phenomenon under study. In this frame-work, we propose to solve the likelihood and the decoding problems of HMMs whose state space is composed of a continuous part and a discrete part. We adapt forward, backward and Viterbi algorithms to the case of our proposal. Numerical examples and Monte Carlo simulations are considered to show the efficiency and the adaptation of the algorithms for the proposed model.