Bayesian Hypothesis Testing on Kendall Rank Correlation Coefficient

• Activity Number: 58 - Advanced Bayesian Topics (Part 1)
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Min Wang* and Keying Ye and Shen Zhang
• Companies: The University of Texas at San Antonio and The University of Texas at San Antonio and The University of Texas at San Antonio
• Keywords: Bayes factor; Kendall's tau; nonparametric hypothesis testing; prior elicitation; consistency

Abstract

In this talk, we propose a Bayesian hypothesis test for the presence of an association between two variables measured on at least an ordinal scale. Owing to the absence of the likelihood function for the data, we consider the sampling distributions of the test statistic and then specify a truncated normal prior for the noncentrality parameter of the test statistic under the alternative hypothesis, which results in a closed-form expression for the Bayes factor. It is shown that the proposed Bayes factor depends on the data only through the standardized version of the Kendall's rank correlation coefficient and can be computed by practitioners with an excel spreadsheet. Furthermore, the results can be easily covered in undergraduate and graduate courses in nonparametric statistics with an emphasis on students' Bayesian thinking and analysis to real-data problems.