Bayesian analysis of a change-point in exponential families with applications

A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential family distributions. The conjugate priors for the exponential families are considered in the analysis. The marginal posterior distribution of the change-point j is derived. Since some hyper-parameters are involved in the conjugate priors, the Type II maximum likelihood (ML-II) approach (cf. Berger, 1995) will be used to estimate these hyperparameters in applications. The method is simple and is easily applied to the Nile problem, Illinois traffic data, British coal-mining disasters, accident data and stock-market prices. (C) 1998 Elsevier Science B.V. All rights reserved.