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.