Bayesian Latent-Normal Inference for the Rank Sum Test, the Signed Rank Test, and Spearman's ρ
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Bayesian inference for rank-order problems is frustrated by the absence of an explicit likelihood function. This hurdle can be overcome by assuming a latent normal representation that is consistent with the ordinal information in the data: the observed ranks are conceptualized as an impoverished reflection of an underlying continuous scale, and inference concerns the parameters that govern the latent representation. We apply this generic data-augmentation method to obtain Bayesian counterparts of three popular rank-based tests: the rank sum test, the signed rank test, and Spearman's ρ.
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