Variational Bayes for Phase-Type Distribution

This article develops an algorithm for estimating parameters of general phase-type (PH) distribution based on Bayes estimation. The idea of Bayes estimation is to regard parameters as random variables, and the posterior distribution of parameters which is updated by the likelihood function provides estimators of parameters. One of the advantages of Bayes estimation is to evaluate uncertainty of estimators. In this article, we propose a fast algorithm for computing posterior distributions approximately, based on variational approximation. We formulate the optimal variational posterior distributions for PH distributions and develop the efficient computation algorithm for the optimal variational posterior distributions of discrete and continuous PH distributions.