Bayesian Rank-Based Hypothesis Testing for the Rank Sum Test, the Signed Rank Test, and Spearman's $\rho$

TL;DR

This paper introduces a Bayesian approach to rank-based hypothesis testing by assuming a latent normal model, enabling the calculation of Bayes factors for common non-parametric tests.

Contribution

It develops a novel data-augmentation method to derive Bayesian inference and Bayes factors for rank sum, signed rank, and Spearman's rho tests.

Findings

Provides a Bayesian framework for rank-based tests

Enables computation of Bayes factors for these tests

Facilitates Bayesian hypothesis testing in ordinal data

Abstract

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 Bayes factors for three popular rank-based tests: the rank sum test, the signed rank test, and Spearman's $\rho_s$.