Markov chain Monte Carlo for Phase-type Inference
Lead PI:Prof. Simon Wilson
Abstract:Bayesian inference for phase-type distributions is considered when data consist only of absorption times. Extensions to the methodology developed by Bladt et al. (2003) are presented which enable specific structure to be imposed on the underlying continuous time Markov process and expand computational tractability to a wider class of situations.The conditions for maintaining conjugacy when structure is imposed are developed. Part of the original algorithm involves simulation of the unobserved Markov process and the main contribution is resolution of computational issues which can arise here.The extended methodology thus improves modelling and tractability of Bayesian inference for phase-type distributions where there is direct scientific interest in the underlying stochastic process: the added structural constraints more accurately represent a physical process and the computational changes make the technique practical to implement. A simple application to a repairable redundant electronic system when ultimate system failure (as opposed to individual component failure) comprise the data is presented. This provides one example of a class of problems for which the extended methodology improves both parameter estimates and computational speed.