Bayesian hypothesis tests using nonparametric statistics

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 non-parametric test statistics having limiting normal distributions and illustrate these methods with data. Finally, we consider the extension of our methodology to non-parametric test statistics having limiting X² distributions.