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 or chi-square distributions. We also demonstrate how this testing strategy can be extended to simplify meta-analyses in which only p values or the values of test statistics have been reported.
Statistical Methodology | Statistical Theory
Yuan, Ying and Johnson, Valen E., "Bayesian Hypothesis Tests Using Nonparametric Statistics" (February 2006). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 21.