A Simple Bayesian Approach to Multiple Change-points

After a brief review of previous frequentist and Bayesian approaches to multiple change-points, we describe a Bayesian model for multiple parameter changes in a multiparameter exponential family. This model has attractive statistical and computational properties and yields explicit recursive formulas for the Bayes estimates of the piecewise constant parameters. Efficient estimators of the hyperparameters of the Bayesian model for the parameter jumps can be used in conjunction, yielding empirical Bayes estimates. The empirical Bayes approach is also applied to solve long-standing frequentist problems such as significance testing of the null hypothesis of no change-points versus multiple change-point alternatives, and inference on the number and locations of change-points that partition the unknown parameter sequence into segments of equal values. Simulation studies of performance and an illustrative application to the British coal mine data are also given. Extensions from the exponential family to general parametric families and from independent observations to genearlized linear time series models are then provided.