Bayesian Calibrated Significance Levels Applied to the Spectral Tilt and Hemispherical Asymmetry

Abstract

Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign them meaningful priors, an essential ingredient of Bayesian model selection. Here we look at methods maximizing the prior so as to work out what is the maximum support the data could give for the new parameters. If the maximum support is not high enough then one can confidently conclude that the new parameters are unnecessary without needing to worry that some other prior may make them significant. We discuss a computationally efficient means of doing this which involves mapping p-values onto upper bounds of the Bayes factor (or odds) for the new parameters. A p-value of 0.05 ($1.96\sigma$) corresponds to odds less than or equal to 5:2 which is below the `weak' support at best threshold. A p-value of 0.0003 ($3.6\sigma$) corresponds to odds of less than or equal to 150:1 which is the `strong' support at best threshold. Applying this method we find that the odds on the scalar spectral index being different from one are 49:1 at best. We also find that the odds that there is primordial hemispherical asymmetry in the cosmic microwave background are 9:1 at best.

5 pages. V2: clarifying comments added in response to referee report. Matches version to appear in MNRAS

References in corpus (8)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
• Local Voids as the Origin of Large-angle Cosmic Microwave Background Anomalies I
• Measuring the effective complexity of cosmological models
• A Bayesian model selection analysis of WMAP3
• A re-analysis of the three-year WMAP temperature power spectrum and likelihood
• Broken Isotropy from a Linear Modulation of the Primordial Perturbations
• Forecasting the Bayes factor of a future observation

Cited by in corpus (26)

• Bayes in the sky: Bayesian inference and model selection in cosmology
• Bayesian Analysis of Inflation: Parameter Estimation for Single Field Models
• Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results
• Detection of Cosmological 21 cm Emission with the Canadian Hydrogen Intensity Mapping Experiment
• Hunting Down the Best Model of Inflation with Bayesian Evidence
• Testable polarization predictions for models of CMB isotropy anomalies
• Reconstruction of the Dark Energy equation of state
• A pair of Sub-Neptunes transiting the bright K-dwarf TOI-1064 characterised with CHEOPS
• Constraints on modified gravity from the BOSS galaxy survey
• 2D Retrieval Frameworks for Hot Jupiter Phase Curves
• Fingerprinting Dark Energy II: weak lensing and galaxy clustering tests
• Cosmic Inflation at the Crossroads
• Should we doubt the cosmological constant?
• Determining the motion of the solar system relative to the cosmic microwave background using type Ia supernovae
• Limitations of Bayesian Evidence Applied to Cosmology
• Mean shift cluster recognition method implementation in the nested sampling algorithm
• Flat Tree-level Inflationary Potentials in Light of CMB and LSS Data
• Constraining f(R) gravity with cross-correlation of galaxies and cosmic microwave background lensing
• Cosmological constraints on a unified dark matter-energy scalar field model with fast transition
• A Framework for Optimizing Exoplanet Target Selection for the James Webb Space Telescope
• Global Bayesian Analysis of $\mathrm{J}/\psi$ Photoproduction on Proton and Lead Targets
• Euclid preparation LXXI. Simulations and nonlinearities beyond $\mathsf{\Lambda }$CDM. 3. Constraints on $f(R)$ models from the photometric primary probes
• Bayesian Model Selection and Uncertainty Propagation for Beam Energy Scan Heavy-Ion Collisions
• Primary Velocity and Orbital Phase Effects on Planetary Detectability from Small Epoch Number Data Sets
• Bayesian leave-one-out cross-validation for astrophysical model comparison using gravitational-wave background data
• A Bayesian Approach for Strong Field QED Tests with He-like Ions