Quantifying dimensionality: Bayesian cosmological model complexities

Abstract

We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a measure of the strength of constraint between prior and posterior, we show that the variance of the Shannon information gives a measure of dimensionality of constraint. We examine this quantity in a cosmological context, applying it to likelihoods derived from Cosmic Microwave Background, large scale structure and supernovae data. We show that this measure of Bayesian model dimensionality compares favourably both analytically and numerically in a cosmological context with the existing measure of model complexity used in the literature.

14 pages, 9 figures. v2: updates post peer-review. v3: typographical correction to equation 35

References in corpus (39)

• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Information criteria for astrophysical model selection
• Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code
• Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
• Efficient sampling of fast and slow cosmological parameters
• A Conceptual Introduction to Hamiltonian Monte Carlo
• New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• Dynamical dark energy in light of the latest observations
• How many cosmological parameters?
• CosmoSIS: modular cosmological parameter estimation
• Galaxy alignments: An overview
• The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology
• KiDS+GAMA: Cosmology constraints from a joint analysis of cosmic shear, galaxy-galaxy lensing and angular clustering
• Concordance and Discordance in Cosmology
• Measuring the effective complexity of cosmological models
• Exploring Cosmic Origins with CORE: Inflation
• anesthetic: nested sampling visualisation
• Bayesian model selection without evidences: application to the dark energy equation-of-state
• Is there concordance within the concordance $\Lambda$CDM model?
• Information Entropy in Cosmology
• Statistical Inconsistencies in the KiDS-450 Dataset
• Information Gain on Reheating: the One Bit Milestone
• Bayesian optimal reconstruction of the primordial power spectrum
• Information Gains from Cosmic Microwave Background Experiments
• Quantifying Tensions between CMB and Distance Datasets in Models with Free Curvature or Lensing Amplitude
• Consistency tests in cosmology using relative entropy
• Quantifying Concordance in Cosmology
• Information Gains from Cosmological Probes
• Cosmology-marginalized approaches in Bayesian model comparison: the neutrino mass as a case study
• Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning
• Integrated cosmological probes: Concordance quantified
• Optimal prior for Bayesian inference in a constrained parameter space

Cited by in corpus (53)

• Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Data Calibration
• Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Modeling Uncertainty
• Curvature tension: evidence for a closed universe
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• The evidence for a spatially flat Universe
• Baryon Acoustic Oscillations and the Hubble Constant: Past, Present and Future
• Arbitrating the $S_8$ discrepancy with growth rate measurements from Redshift-Space Distortions
• DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys
• KiDS+VIKING-450 and DES-Y1 combined: Mitigating baryon feedback uncertainty with COSEBIs
• KiDS-1000 Methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis
• Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio
• Using non-DESI data to confirm and strengthen the DESI 2024 spatially-flat $w_0{w}_a$CDM cosmological parameterization result
• Detection of Cosmological 21 cm Emission with the Canadian Hydrogen Intensity Mapping Experiment
• Assessing tension metrics with Dark Energy Survey and Planck data
• Quantifying the global parameter tensions between ACT, SPT and Planck
• Return of Harrison-Zeldovich spectrum in light of recent cosmological tensions
• Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_{\nu }$: Effects of uniform vs logarithmic priors
• Constraining the Baryonic Feedback with Cosmic Shear Using the DES Year-3 Small-Scale Measurements
• Robust sampling for weak lensing and clustering analyses with the Dark Energy Survey
• Quantifying Suspiciousness Within Correlated Data Sets
• Global fits of axion-like particles to XENON1T and astrophysical data
• The Dark Energy Survey: Cosmology Results With ~1500 New High-redshift Type Ia Supernovae Using The Full 5-year Dataset
• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Cosmic Inflation at the Crossroads
• Is the $w_0{w}_a$CDM cosmological parameterization evidence for dark energy dynamics partially caused by the excess smoothing of Planck CMB anisotropy data?
• KiDS-Legacy: Consistency of cosmic shear measurements and joint cosmological constraints with external probes
• DES Y1 results: Splitting growth and geometry to test $\Lambda$CDM
• Use of Time Dependent Data in Bayesian Global 21cm Foreground and Signal Modelling
• Current data are consistent with flat spatial hypersurfaces in the $\Lambda$CDM cosmological model but favor more lensing than the model predicts
• Self-calibration and robust propagation of photometric redshift distribution uncertainties in weak gravitational lensing
• When tension is just a fluctuation: How noisy data affect model comparison
• On dataset tensions and signatures of new cosmological physics
• Exploring phase space with Nested Sampling
• KiDS+VIKING-450: An internal-consistency test for cosmic shear tomography with a colour-based split of source galaxies
• Constraints on Equivalence Principle Violation from Gamma Ray Bursts
• Marginal Bayesian Statistics Using Masked Autoregressive Flows and Kernel Density Estimators with Examples in Cosmology
• DHOST gravity in Ultra-diffuse galaxies -- Part II: NGC 1052-DF4 and Dragonfly 44
• Cosmic dipole tensions: confronting the cosmic microwave background with infrared and radio populations of cosmological sources
• Constraining Cosmology With the CMB $\times$ LIM-Nulling Convergence
• Convergent Bayesian Global Fits of 4D Composite Higgs Models
• Thawing Quintessence: Priors, evidence, and likely trajectories
• Updated observational constraints on $\varphi$CDM dynamical dark energy cosmological models
• Partition function approach to non-Gaussian likelihoods: Formalism and expansions for weakly non-Gaussian cosmological inference
• Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference
• KiDS-Legacy: Constraining dark energy, neutrino mass, and curvature
• Alleviating the Hubble tension with Torsion Condensation (TorC)
• Dusty Clump Survival in Supernova Ejecta: Dust-Mediated Growth vs. Crushing by the Reverse Shock
• Geometry vs growth: Internal consistency of the flat ΛCDM model with KiDS-1000
• Inferring Evidence from Nested Sampling Data via Information Field Theory
• Finite inflation in curved space
• Towards a Field Based Bayesian Evidence Inference from Nested Sampling Data
• Sector-Resolved Bayesian Model Averaging for DESI-Era Cosmology
• A Comprehensive Bayesian re-analysis of the SARAS2 data from the Epoch of Reionization