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APPROXIMATION OF THE POSTERIOR DISTRIBUTION

IN A CHANGE-POINT PROBLEM

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

^{1} *Division of Theoretical Statistics and Mathematics, Indian Statistical Institute,*

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

^{2} *Computer 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
*theta*. 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 *theta*. 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.

**Source**
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