Phase-type regression models
Seminar in Insurance and Economics
SPEAKER: Jorge Yslas (University of Liverpool).
TITLE: Phase-type regression models.
ABSTRACT: A phase-type (PH) distribution is defined as the distribution of the time until absorption of a time-homogeneous Markov jump process. These distributions have been employed in various contexts since they often provide exact (or even explicit) solutions to relevant problems in complex stochastic models. Moreover, they form a dense class in the class of distributions with support on the positive reals. However, the literature regarding PH distributions in a regression setting is somewhat limited. In this talk, we present three recent models that allow for regression based on PH distributions and their inhomogeneous extension, namely the inhomogeneous phase-type (IPH) distributions. More specifically, we review the proportional intensities model, the phase-type mixture-of-experts model, and the phase-type frailty model. We give some relevant properties of these three models and show how maximum-likelihood estimation can be carried out via modified EM algorithms. Finally, we illustrate their use with both real-life and synthetic data.