An Application of EM Test for the Bayesian Change Point Problem

In any manufacturing process, identification of changes in the process conditions is of great interest. Recently, a Bayesian approach for the identification of the change in process mean was proposed assuming that the response of interest follow an exponential family distribution. In this approach, the expectation – maximization (EM) algorithm was used for estimating the process parameters. In general, the EM algorithm is computationally intensive and the optimality depends on the initial values of the parameters chosen. We extend the idea of the EM test for homogeneity to extend this Bayesian approach to the change point problem. Our simulations studies show that the developed EM test procedure converges at a faster rate than the original EM approach. Our studies also show that the EM test with binomial prior distribution leads to solutions very close to the true values. We have applied our approach to two case examples.