Statistics Seminars: Markov Chain Monte Carlo for Inference on Phase-Type Models
5 April 2012 15:00 in CM221
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 shown. 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. Direct conditional simulation, together with exploiting reversibility when available underpin the changes. Ultimately, several variants of the algorithm are produced, their relative merits explained and guidelines for variant selection provided.
The extended methodology thus advances 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.
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