A Bayesian quantification of consistency in correlated datasets

  title={A Bayesian quantification of consistency in correlated datasets},
  author={Fabian Kohlinger and Benjamin Joachimi and Marika Asgari and Massimo Viola and Shahab Joudaki and Tilman Troster},
  journal={Monthly Notices of the Royal Astronomical Society},
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… 

Quantifying concordance of correlated cosmological data sets

The suite of best estimators that are discussed finds results that are in excellent agreement between estimators and find no indications of significant internal inconsistencies in this data set above the $1\%$ probability threshold.

Quantifying Suspiciousness within correlated data sets

We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which

Dark energy survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

Beyond-$\Lambda$CDM physics or systematic errors may cause subsets of a cosmological data set to appear inconsistent when analyzed assuming $\Lambda$CDM. We present an application of internal

A Bayesian interpretation of inconsistency measures in cosmology

A Bayesian interpretation of inconsistency measures that can extract information about physical inconsistencies in the presence of data scatter is proposed based on the conditional probability distribution of the level of physical inconsistency given the obtained value of the measure.

Cosmological discordances. III. More on measure properties, large-scale-structure constraints, the Hubble constant and Planck data

Consistency between cosmological data sets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based

KiDS+VIKING-450: An internal-consistency test for cosmic shear tomography with a colour-based split of source galaxies

We performed an internal-consistency test of the KiDS+VIKING-450 (KV450) cosmic shear analysis with a colour-based split of source galaxies. Utilising the same measurements and calibrations for both

Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio

The Dark Energy Survey (DES) first year analysis is concluded that DES and Planck are, in a Bayesian sense, incompatible under LCDM, and the Bayesian model dimensionality is introduced in a cosmological setting.

Remarks on measures of inconsistency

This work discusses, with illustrative examples, some requirements that should be fulfilled in Gaussian cases by inconsistency measures and suggests a guiding definition of (in)consistency, and examines the common practice to convert some measures to a probability to exceed or a significance level that depends on the number of parameters.

When tension is just a fluctuation

Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy

Concordance cosmology?

We propose a new intuitive metric for evaluating the tension between two experiments, and apply it to several data sets. While our metric is non-optimal, if evidence of tension is detected, this



Bayesian evidence as a tool for comparing datasets

A conservative test for quantifying the consistency of two or more datasets is introduced and it is found that concordance is favored and the tightening of constraints on cosmological parameters is indeed justified.

Statistical inconsistencies in the KiDS-450 data set

The Kilo-Degree Survey (KiDS) has been used in several recent papers to infer constraints on the amplitude of the matter power spectrum and matter density at low redshift. Some of these analyses have

Withdrawn as Duplicate: Survey geometry and the internal consistency of recent cosmic shear measurements

We explore the impact of an update to the typical approximation for the shape noise term in the analytic covariance matrix for cosmic shear experiments that assumes the absence of survey boundary and

Cosmological discordances: A new measure, marginalization effects, and application to geometry versus growth current data sets

The continuous progress toward more precise cosmological surveys and experiments has galvanized recent interest into consistency tests on cosmological parameters and models. At the heart of this

The power of Bayesian evidence in astronomy

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of

KiDS-450: testing extensions to the standard cosmological model

We test extensions to the standard cosmological model with weak gravitational lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). In these extended cosmologies,

KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters

We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three

Concordance and discordance in cosmology

A full set of estimators of internal and mutual agreement and disagreement, whose strengths complement each other are developed, which allow to take into account the effect of prior information and compute the statistical significance of both tensions and confirmatory biases.

A new measure of tension between experiments

Tensions between cosmological measurements by different surveys or probes have always been important —and are presently much discussed —as they may lead to evidence of new physics. Several tests have

Cosmological discordances II: Hubble constant, Planck and large-scale-structure data sets

We examine systematically the (in)consistency between cosmological constraints as obtained from various current data sets of the expansion history, Large Scale Structure (LSS), and Cosmic Microwave