A Bayesian interpretation of inconsistency measures in cosmology

Abstract

Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of inconsistency measures that can extract information about physical inconsistencies in the presence of data scatter. The new framework is based on the conditional probability distribution of the level of physical inconsistency given the obtained value of the measure. We use the index of inconsistency as a case study to illustrate the new interpretation framework, but this can be generalized to other metrics. Importantly, there are two aspects in the quantification of inconsistency that behave differently as the number of model parameters increases. The first is the probability for the level of physical inconsistency to reach a threshold which drops with the increase of the number of parameters under consideration. Then the second is the actual level of physical inconsistency which remains rather insensitive to such an increase in parameters. This often-overlooked ambiguity leads to an underestimation of the physical inconsistency by the commonly adopted significance level when used, but is resolved by the Bayesian interpretation because the conditional probability distribution includes all the statistical information of the level of physical inconsistency. Finally, we apply the Bayesian interpretation to examine the (in)consistency between Planck versus the Cepheid-based local measurement, the Dark Energy Survey (DES), the Atacama Cosmology Telescope (ACT) and WMAP. We confirm and revisit the degrees of previous physical inconsistencies and show the stability of the new interpretation to the number of cosmological parameters compared to the commonly used n-$\sigma$ interpretation when applied to cosmological tensions in multi-parameter spaces.

Matches JCAP published version. This paper proposes a novel Bayesian method to interpret the significance of inconsistency measures and resolves a long-standing ambiguity in the field

References in corpus (60)

• Tensions between the Early and the Late Universe
• H0LiCOW XIII. A 2.4% measurement of $H_0$ from lensed quasars: $5.3\sigma$ tension between early and late-Universe probes
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints
• Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear
• The Atacama Cosmology Telescope: DR4 Maps and Cosmological Parameters
• One percent determination of the primordial deuterium abundance
• New physics in light of the $H_0$ tension: an alternative view
• Dynamical dark energy in light of the latest observations
• Testing General Relativity in Cosmology
• Reconciling Planck with the local value of $H_0$ in extended parameter space
• Dark energy two decades after: Observables, probes, consistency tests
• Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially-Flat $\Lambda$cdm Model, The Deceleration-Acceleration Transition Redshift, and Spatial Curvature
• CFHTLenS revisited: assessing concordance with Planck including astrophysical systematics
• $H_0$ from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method
• Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models
• Evolution of the $f{\sigma }_8$ tension with the Planck15/$\Lambda$CDM determination and implications for modified gravity theories
• Concordance and Discordance in Cosmology
• Quantifying discordance in the 2015 Planck CMB spectrum
• Constraining the Self-Interacting Neutrino Interpretation of the Hubble Tension
• The $H_0$ tension in light of vacuum dynamics in the Universe
• KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear
• Tension between the power spectrum of density perturbations measured on large and small scales
• Observational constraints on one-parameter dynamical dark-energy parametrizations and the $H_0$ tension
• Tension with the flat ΛCDM model from a high redshift Hubble Diagram of supernovae, quasars and gamma-ray bursts
• Testing the statistical compatibility of independent data sets
• Determining the Hubble constant from Hubble parameter measurements
• Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio
• Using the tilted flat-$\Lambda$CDM and the untilted non-flat $\Lambda$CDM inflation models to measure cosmological parameters from a compilation of observational data
• Bayesian evidence as a tool for comparing datasets
• Density perturbations for running vacuum: a successful approach to structure formation and to the ${\sigma }_8$-tension
• Novel approach towards the large-scale stable Interacting Dark-Energy models and their Astronomical Bounds
• How the Dark Energy Can Reconcile \textit{Planck} with Local Determination of the Hubble Constant
• Emerging spatial curvature can resolve the tension between high-redshift CMB and low-redshift distance ladder measurements of the Hubble constant
• Assessing tension metrics with Dark Energy Survey and Planck data
• Quantifying the global parameter tensions between ACT, SPT and Planck
• Cosmological discordances II: Hubble constant, Planck and large-scale-structure data sets
• Model-independent determination of $H_0$ and ${\Omega }_{K0}$ from strong lensing and type Ia supernovae
• Cosmological discordances: a new measure, marginalization effects, and application to geometry vs growth current data sets
• Observational constraints on the tilted flat-XCDM and the untilted nonflat XCDM dynamical dark energy inflation parameterizations
• Planck 2015 constraints on the non-flat XCDM inflation model
• Information Gains from Cosmic Microwave Background Experiments
• Planck confronts large scale structure: methods to quantify discordance
• Consistency tests in cosmology using relative entropy
• Consistency of the local Hubble constant with the cosmic microwave background
• Unveiling the Intrinsic Alignment of Galaxies with Self-Calibration and DECaLS DR3 data
• The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
• Investigating the Hubble Constant Tension -- Two Numbers in the Standard Cosmological Model
• Robustness to systematics for future dark energy probes
• Quantifying Concordance in Cosmology
• Information Gains from Cosmological Probes
• A new measure of tension between experiments
• Isotropic vs. Anisotropic components of BAO data: a tool for model selection
• Effect of inhomogeneities on high precision measurements of cosmological distances
• Concordance Cosmology?
• A Bayesian quantification of consistency in correlated datasets
• Cosmological discordances III: more on measure properties, Large-Scale-Structure constraints, the Hubble constant and Planck
• Limitations of Bayesian Evidence Applied to Cosmology
• Phantom Dirac-Born-Infeld Dark Energy

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• Holographic and Gravity-Thermodynamic Approaches in Entropic Cosmology: Bayesian Assessment using late-time Data
• Tracking the Multifield Dynamics with Cosmological Data: A Monte Carlo approach
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Stability analysis of warm quintessential dark energy model
• How robust are the parameter constraints extending the $\Lambda$CDM model?
• Dynamical dark energy can amplify the expansion rate of the Universe
• ${\Lambda }_{\mathrm{s}}$CDM cosmology from a type-II minimally modified gravity
• Uncalibrated Cosmic Standards as a Robust Test on Late-Time Cosmological Models
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• One Extension to Explain Them All, One Scale-Invariant Spectrum to Test Them All, and in One Model Bind Them
• Constraints on the Hubble and matter density parameters with and without modelling the CMB anisotropies
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