A Bayesian multiple comparison procedure for ranking the means of normally distributed data

We present a Bayesian decision-theoretic model for producing, via all pair-wise comparisons, a set of possible rankings for a given number of normal means. A simulation is performed to compare this constant loss model to popular frequentist methods used to rank normal means, including Tukeys method and the Benjamini-Hochberg procedure. The model will also be compared to a Bayesian model using a linear loss function. Properties to be compared include the probability of containing the true ranking and the expected number of possible rankings produced.