BAYESIAN-ESTIMATION OF THE NUMBER OF CHANGE-POINTS

The problem of estimating the number of change points in a sequence of independent random variables is considered in a Bayesian framework. W e find that, under mild assumptions and with respect to a suitable pri or distribution, the posterior mode of the number of change points con verges to the true number of change points in the frequentist sense. F urthermore, the posterior mode of the locations of the change points i s shown to be within O-p(log n) of the true locations of the change po ints where n is the sample size. The prior distribution on the locatio ns of the change points may be taken to be uniform. Finally, some simu lated results are given, showing that the method works well in estimat ing the number of change points.