Bayesian Inference for Censored Observations: Posterior Inconsistency and Its Remedy

In Bayesian paradigm of survival analysis, we can combine a nonparametric estimator and a parametric model by putting a prior distribution nonparametrically around the entire parametric family. This method can avoids the ineeciency of the nonparametric estimator due to ignoring partial information about a parametric model and at the same time avoids the pitfalls connected with an incorrectly speciied parametric model. In this paper, it is shown that the additional eeciency of using a parametric model may not come true in general by presenting an example in which the posterior distribution of the parametric model is not consistent. Then a Bayesian model is suggested in which the posterior distribution of the parametric model is consistent. Finally, our results are illustrated in a real data set.