We propose two new classes of Bayesian measure to investigate conflict among data sets from multiple studies. The first (“concentration ratio”) is used to quantify the amount of information provided by a single data set through the comparison of the prior and its posterior distribution, or two data sets according to their corresponding posterior distributions. The second class (“dissonance”) quantifies the extent of contradiction between two data sets. Both classes are based on volumes of highest density regions. They are well calibrated, supported by simulation, and computational algorithms are provided for their calculation. We illustrate these two classes in three real data applications: a benchmark dose toxicology study, a missing data study related to health effects of pollution, and a pediatric cancer study leveraging adult data.
This material is based upon work supported by the National Science Foundation under Grant No. DEB-1354146. Dr. M.-H. Chen’s research was also partially supported by NIH grants #GM70335 and #P01CA142538.
We would like to thank the editor, associate editor, and two reviewers for many helpful comments which help to improve the paper tremendously.
Wei Shi. Ming-Hui Chen. Lynn Kuo. Paul O. Lewis. "Bayesian Concentration Ratio and Dissonance." Bayesian Anal. 17 (3) 817 - 847, September 2022. https://doi.org/10.1214/21-BA1277