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

Abstract

The hazard rate h(t) of a lifetime random variable is assumed to be a constant equal to a up to time r and another constant equal to b thereafter. The parameters T and (a, b) are assumed to be independent apriori with r having a uniform prior on [t₁, t₂], 0 < t₁ < t₂ < ∞ while the prior of (a, b) is assumed to be smooth, It is proved that the marginal posterior mode of r is n-consistent; the marginal posterior mass of T 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 T are asymptotically independent aposieriori; 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.