Date of Award


Document Type

Open Access Dissertation



First Advisor

Edsel A. Peña


This dissertation deals with non- and semi-parametric Bayesian inference of gap-time distribution with recurrent event data and simultaneous inference of component and system reliabilities of coherent systems data. Recurrent event data arise from a wide variety of studies/fields such as clinical trials, epidemiology, public health, biomedicine (e.g. repeated heart attack, repeated tumor occurrences of a cancer patient). In Chapter 2 we develop nonparametric Bayes and empirical Bayes estimators of the survivor function \bar{F} = 1 - F, of the gap-time distribution by assigning a Dirichlet process prior on F. We develop a closed form estimator of \bar{F} as well as a procedure to sample from the posterior measure and thus construct point-wise credible intervals. Semiparametric Bayesian inference of the gap-time survivor function with the effect of covariates of a correlated recurrent event in the presence of censoring is considered in Chapter 3. A frailty model is considered to allow the association between inter-occurrence gap-times. We assign a gamma process prior on the baseline cumulative hazard function &Lambda 0 <\sub> and parametric prior distributions on the finite dimensional parameters associated with covariates and frailties. We derive the conditional posterior distributions of the unknown parameters of interest from the joint posterior distribution and employ Gibbs sampling techniques to obtain samples from the joint posterior distribution. In Chapter 4 we focus on nonparametric Bayesian inference of reliability of coherent systems which are prevalent in many settings such as in mechanical, engineering, military, and financial systems. In our nonparametric Bayesian approach we assign independent partition-based Dirichlet (PBD) priors, on the component distribution functions. A simultaneous inference procedure of component and system reliabilities is developed. Bayesian paradigm provides a more general estimator in the sense that we can recover corresponding nonparametric estimators as a limiting case of our developed estimators both in recurrent event and reliability settings.