A Bayesian quantification of consistency in correlated data sets
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 σ in all cases. Software and data used in this analysis can be found at http://kids.strw.leidenuniv.nl/sciencedata.php.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- April 2019
- DOI:
- 10.1093/mnras/stz132
- arXiv:
- arXiv:1809.01406
- Bibcode:
- 2019MNRAS.484.3126K
- Keywords:
-
- gravitational lensing: weak;
- methods: data analysis;
- statistical;
- cosmology: cosmological parameters;
- observations;
- large-scale structure of Universe;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- Accepted by MNRAS. Conclusions unchanged with respect to v1, but now a more pedagogical introduction to all consistency tests is included in (new) Section 3. Software and data used in this analysis are available at http://kids.strw.leidenuniv.nl/sciencedata.php