Planck confronts large scale structure: methods to quantify discordance
  Discordance in the $\Lambda$CDM cosmological model can be seen by comparing
parameters constrained by CMB measurements to those inferred by probes of large
scale structure. Recent improvements in observations, including final data
releases from both Planck and SDSS-III BOSS, as well as improved astrophysical
uncertainty analysis of CFHTLenS, allows for an update in the quantification of
any tension between large and small scales. This paper is intended, primarily,
as a discussion on the quantifications of discordance when comparing the
parameter constraints of a model when given two different data sets. We
consider KL-divergence, comparison of Bayesian evidences and other statistics
which are sensitive to the mean, variance and shape of the distributions.
However, as a by-product, we present an update to the similar analysis in
(Battye, Charnock and Moss; 2015) where we find that, considering new data and
treatment of priors, the constraints from the CMB and from a combination of LSS
probes are in greater agreement and any tension only persists to a minor
degree. In particular, we find the parameter constraints from the combination
of LSS probes which are most discrepant with the Planck2015+Pol+BAO parameter
distributions can be quantified at a 2.55$\sigma$ tension using the method
introduced in (Battye, Charnock and Moss; 2015). If instead we use the
distributions constrained by the combination of LSS probes which are in
greatest agreement with those from Planck2015+Pol+BAO this tension is only
0.76$\sigma$.
