On posterior consistency of survival models

Abstract

Ghosh and Ramamoorthi studied posterior consistency for survival models and showed that the posterior was consistent when the prior on the distribution of survival times was the Dirichlet process prior. In this paper,we study posterior consistency of survival models with neutral to the right process priors which include Dirichlet process priors. A set of sufficient conditions for posterior consistency with neutral to the right process priors are given. Interestingly, not all the neutral to the right process priors have consistent posteriors, but most of the popular priors such as Dirichlet processes, beta processes and gamma processes have consistent posteriors. With a class of priors which includes beta processes, a necessary and sufficient condition for the consistency is also established. An interesting counter-intuitive phenomenon is found. Suppose there are two priors centered at the true parameter value with finite variances. Surprisingly, the posterior with smaller prior variance can be inconsistent, while that with larger prior variance is consistent.