A Bayesian quantification of consistency in correlated data sets

Journal article

We present three tiers of Bayesian consistency tests for the general case of correlated data sets. Building on duplicates of the model parameters assigned to each data set, these tests range from Bayesian evidence ratios as a global summary statistic, to posterior distributions of model parameter differences, to consistency tests in the data domain derived from posterior predictive distributions. For each test, we motivate meaningful threshold criteria for the internal consistency of data sets. Without loss of generality we focus on mutually exclusive, correlated subsets of the same data set in this work. As an application, we revisit the consistency analysis of the two-point weak-lensing shear correlation functions measured from KiDS-450 data. We split this data set according to large versus small angular scales, tomographic redshift bin combinations, and estimator type. We do not find any evidence for significant internal tension in the KiDS-450 data, with significances below 3σ in all cases. Software and data used in this analysis can be found at http://kids.strw.leidenuniv.nl/sciencedata.php.

Authors: Kohlinger, F; Joachimi, B; Asgari, M; Viola, M; Joudaki, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Oxford University Press
• Journal: Monthly Notices of the Royal Astronomical Society
• Volume: 484
• Issue: 3
• Pages: 3126-3153
• Publication date: 2019-01-16
• Acceptance date: 2020-01-09
• DOI: 10.1093/mnras/stz132
• EISSN: 1365-2966
• ISSN: 0035-8711
• Language: English
• Keywords: cosmology: cosmological parameters; large-scale structure of universe; methods: data analysis; observations; FFR; gravitational lensing: weak; statistical