A Markov Chain Monte Carlo Procedure for Efficient Bayesian Inference on the Phase-Type Aging Model

The phase-type aging model (PTAM) belongs to a class of Coxian-type Markovian models that can provide a quantitative description of well-known aging characteristics that are part of a genetically determined, progressive, and irreversible process. Due to its unique parameter structure, estimation via the MLE method presents a considerable estimability issue, whereby profile likelihood functions are flat and analytically intractable. In this study, a Markov chain Monte Carlo (MCMC)-based Bayesian methodology is proposed and applied to the PTAM, with a view to improving parameter estimability. The proposed method provides two methodological extensions based on an existing MCMC inference method. First, we propose a two-level MCMC sampling scheme that makes the method applicable to situations where the posterior distributions do not assume simple forms after data augmentation. Secondly, an existing data augmentation technique for Bayesian inference on continuous phase-type distributions is further developed in order to incorporate left-truncated data. While numerical results indicate that the proposed methodology improves parameter estimability via sound prior distributions, this approach may also be utilized as a stand-alone statistical model-fitting technique.