On the reversibility of the observed process of three-state hidden Markov model

TL;DR

This paper explicitly derives the likelihood flux for three-state hidden Markov models in continuous and discrete time, and establishes conditions for the reversibility of the observed process.

Contribution

It provides a novel explicit expression for likelihood flux and characterizes the reversibility condition for three-state hidden Markov models.

Findings

Explicit likelihood flux formulas for 3D observed process

Necessary and sufficient conditions for reversibility

Application to continuous and discrete-time models

Abstract

For the continuous-time and the discrete-time three-state hidden Markov model, the flux of the likelihood function up to 3-dimension of the observed process is shown explicitly. As an application, the sufficient and necessary condition of the reversibility of the observed process is shown.