A Bayesian Comparison of k Exponential Means Using the Mixture of Dirichlet Process Prior

In this article, we suggest a semi-nonparametric Bayesian method for calculating posterior probabilities for various hypotheses of equality among k exponential populations. This leads to a simple method for obtains pairwise comparisons of means in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships among the means. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combination to provide the method. Finding the posterior probabilities are analytically intractable, we use Gibbs sampling. A simulation study is illustrated for the method. It is seen that the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required comparison.