Maximum Likelihood Estimation for Scaled Inhomogeneous Phase-Type Distributions from Discrete Observations
Published in arXiv, 2025
Recommended citation: Baltazar-Larios, F., Quintos, A. Maximum Likelihood Estimation for Scaled Inhomogeneous Phase-Type Distributions from Discrete Observations. Preprint (2025). https://arxiv.org/abs/2512.16061
Inhomogeneous phase-type (IPH) distributions extend classical phase-type models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed or time-dependent absorption phenomena. We focus on the subclass of IPH distributions with time-scaled sub-intensity matrices of the form Λ(t)=h_β(t)Λ, which admits a time transformation to a homogeneous Markov jump process. For this class, we develop a statistical inference framework for discretely observed trajectories that combines Markov-bridge reconstruction with a stochastic EM algorithm and a gradient-based update. The resulting method yields joint maximum-likelihood estimates of both the baseline sub-intensity matrix Λ and the time-scaling parameter β. Through simulation studies for the matrix-Gompertz and matrix-Weibull families, and a real-data application to coronary allograft vasculopathy progression, we demonstrate that the proposed approach provides an accurate and computationally tractable tool for fitting time-scaled IPH models to irregular multi-state data.