Asymptotics of a Bayesian approach to estimating change-point in a hazard rate

The hazard rate h(t) of a lifetime random variable is assumed to be a constant equal to a up to time tau and another constant equal to b thereafter. The parameters tau and (a, b) are assumed to be independent apriori, with tau having a uniform prior on [t(1), t(2)], 0 < t(1) < t(2) < infinity, while the prior of (a, b) is assumed to be smooth. It is proved that the marginal posterior mode of tau is n-consistent; the marginal posterior mass of tau is concentrated around an n(-1) neighborhood of the unknown parameter value; the posterior distribution of (a,b) can be approximated by a Normal distribution; a, b tau are asymptotically independent aposteriori; and one can approximate the posterior mean and variance of (a,b) by easily computable quantities. The accuracies of these approximations are examined by a simulation study.