Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ

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 ref...

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Bibliographic Details
Published in:Journal of applied statistics 2020-12, Vol.47 (16), p.2984-3006
Main Authors: van Doorn, J., Ly, A., Marsman, M., Wagenmakers, E.-J.
Format: Article
Language:English
Subjects:
Bayes factors
Bayesian analysis
data augmentation
Hypothesis testing
latent normal
Rank tests
Representations
semi-parametrics
Statistical inference
Statistical methods
two-sample
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Summary: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 .
ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2019.1709053