Likelihood Computations for Extended Poisson Process Models

Abstract

Some computational aspects of maximum likelihood estimation for extended Poisson process models are discussed, with computation of log-likelihood derivatives being of particular interest. A method is proposed for computation of these derivatives that involves extending the matrix of transition rates describing the underlying stochastic process. This scheme is designed for parametric forms of the transition rates that can include covariate dependence. Keywords: extended Poisson process models, matrix of transition rates, expokit, maximum likelihood estimation Current address: School of Applied Mathematics and Statistics, Griffith University, Brisbane, Australia. y Current address: Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. 1 1 Introduction Extended Poisson process models provide a general framework for the analysis of discrete data (Faddy, 1997a, 1997b, 1998). They involve representing a discrete distribution as the distributi...