APPROXIMATION OF THE POSTERIOR DISTRIBUTION IN A CHANGE-POINT PROBLEM

SUBHASHIS GHOSAL^{1}, JAYANTA K. GHOSH^{1} AND TAPAS SAMANTA^{2}

1Division of Theoretical Statistics and Mathematics, Indian Statistical Institute,

203 B. T. Road, Calcutta-700035, India

2Computer Science Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta-700035, India

(Received March 8, 1996; revised February 2, 1998)

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.

Key words and phrases: Change-point, Gibbs sampling, hazard rate, posterior distribution.