Approximation of the posterior distribution in a change-point problem

Abstract

We consider a family of models that arise in connection with sharp change in hazard rate corresponding to high initial hazard rate dropping to a more stable or slowly changing rate at an unknown change-point θ. Although the Bayes estimates are well behaved and are asymptotically efficient, it is difficult to compute them as the posterior distributions are generally very complicated. We obtain a simple first order asymptotic approximation to the posterior distribution of θ. The accuracy of the approximation is judged through simulation. The approximation performs quite well. Our method is also applied to analyze a real data set.