An efficient algorithm for computation of information matrix in phase-type fitting

Abstract

Abstract Phase-type (PH) fitting is a technique to approximate any general distribution as a PH distribution, which is a probability distribution representing an absorbing time of a Markov chain. Since the PH distribution is described as a discrete- or continuous-time Markov chain (CTMC), the PH fitting can provide approximate Markov models to any non-exponential stochastic models. Thus, the PH fitting is helpful for model-based performance evaluation. On the other hand, from the statistical point of view, the PH fitting is categorized as parameter estimation from data. Some efficient PH fitting techniques are based on the maximum-likelihood principle. Therefore, it is crucial to evaluate statistical errors, i.e., the variance and covariance of estimators. In maximum-likelihood estimation, the Fisher information matrix is a well-known method to compute the variance and covariance of estimators, and is obtained as the second derivative of the log-likelihood function (LLF). In this article, we propose an algorithm for efficiently computing the Fisher information matrix in PH fitting. By applying the uniformization technique to a CTMC, we design the algorithm for computing the second derivatives of LLF in PH fitting.