PhD Thesis Defence Public Lecture (DSAS) - Cong Nie

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In particular, this objectivity is achieved via a carefully designed c.d.f. sensitivity measure, under which the threshold will become an experiment-based quantity. The proposed measure which is validated to be innately sound, is then applied to assess and improve the estimability of several statistical models, the focus being placed on the PTAM.

Secondly, Markov chain Monte Carlo (MCMC) algorithms are proposed for inference on the PTAM and the DMPTM. Up to now, the MCMC algorithms for continuous phase-type distributions have been applied via the Gibbs sampler which consists of two iterative steps: a data augmentation step and a posterior sampling step. However, owing to unique structures of the PTAM and the DMPTM, this Gibbs sampler turns out to be inadequate, giving rise to problems occurring in either the data augmentation step or the posterior sampling step. To circumvent these difficulties, we methodologically extend the existing Gibbs sampling methodology in terms of rejection sampling and data cloning. The proposed algorithms are then applied to calibrate the PTAM and the DMPTM based on simulated and real-life data. Experimental results show that the proposed MCMC algorithms, as a stochastic approximation technique, achieve estimation results that are comparable to those obtained by deterministic approximation techniques, which can also be seen as a contribution made to the field of approximate inference.