A Bayesian quantification of consistency in correlated datasets
  We present three tiers of Bayesian consistency tests for the general case of
$correlated$ datasets. Building on duplicates of the model parameters assigned
to each dataset, 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 datasets. Without loss of generality we focus on
mutually exclusive, correlated subsets of the same dataset 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 dataset
according to large vs. 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
