On Bayesian selection of the best normal population using theKullback–Leibler divergence measure

In this paper, we use the Bayesian approach to study the problem of selecting the best population among k different populations π 1 , ..., π k (k≥2) relative to some standard (or control) population π 0 . Here, π 0 is considered to be the population with the desired characteristics. The best population is defined to be the one which is closest to the ideal population π 0 . The procedure uses the idea of minimizing the posterior expected value of the Kullback–Leibler (KL) divergence measure of π i from π 0 . The populations under consideration are assumed to be multivariate normal. An application to regression problems is also presented. Finally, a numerical example using real data set is provided to illustrate the implementation of the selection procedure.