Bayesian R-estimates in two-sample location models

Implementation of nonparametric rank-based procedures in the Bayesian context is discussed primarily for the two-sample location models. The information in the data is summarized via the (possibly asymptotic) distribution of some rank-based quantity, which is used as a pseudo-likelihood. The complete posterior distribution (or the posterior distribution up to a normalizing constant) of the parameter of interest given the rank-based quantity can be obtained by assuming a prior distribution for the parameter. Statistical inference then proceeds based on this posterior distribution. Posterior estimation and testing are considered, along with a discussion of a normal approximation to the posterior distribution.