A Bayesian quantification of consistency in correlated data sets. Issue 3 (16th January 2019)

• Record Type: Journal Article
• Authors: Köhlinger, Fabian; Joachimi, Benjamin; Asgari, Marika; Viola, Massimo; Joudaki, Shahab; Tröster, Tilman
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 484:Issue 3(2019)
• Page Start: 3126
• Page End: 3153
• Publication Date: 2019-01-16
• Subjects: gravitational lensing: weak -- methods: data analysis -- statistical -- cosmology: cosmological parameters -- observations -- large-scale structure of Universe; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stz132
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: 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 $3\, \sigma$ in all cases. Software and data used in this analysis can be found at http://kids.strw.leidenuniv.nl/sciencedata.php .