Abstract: Traditionally, the application of Bayesian testing procedures to classical nonparametric settings has been restricted by difficulties associated with prior specification, prohibitively expensive computation, and the absence of sampling densities for data. To overcome these difficulties, we model the sampling distributions of nonparametric test statistics--rather than the sampling distributions of original data--to obtain the Bayes factors required for Bayesian hypothesis tests. We apply this methodology to construct Bayes factors from a wide class of nonparametric test statistics having limiting normal distributions and illustrate these methods with data. Finally, we consider the extension of our methodology to nonparametric test statistics having limiting distributions.
Key words and phrases: Bayes factor, Kruskal-Wallis test, Logrank test, Mann-Whitney-Wilcoxon test, nonparametric hypothesis test, Wilcoxon signed rank test.