Calculating Bayesian evidence for inflationary models using CONNECT

Abstract

Bayesian evidence is a standard tool used for comparing the ability of different models to fit available data and is used extensively in cosmology. However, since the evidence calculation involves performing an integral of the likelihood function over the entire space of model parameters this can be prohibitively expensive in terms of both CPU and time consumption. For example, in the simplest $\Lambda$CDM model and using CMB data from the Planck satellite, the dimensionality of the model space is over 30 (typically 6 cosmological parameters and 28 nuisance parameters). Even the simplest possible model requires $\mathcal{O}(10^6)$ calls to an Einstein--Boltzmann solver such as CLASS or CAMB and takes several days. Here we present calculations of Bayesian evidence using the CONNECT framework to calculate cosmological observables. We demonstrate that we can achieve results comparable to those obtained using Einstein--Boltzmann solvers, but at a minute fraction of the computational cost. As a test case, we then go on to compute Bayesian evidence ratios for a selection of slow-roll inflationary models. In the setup presented here, the total computation time is completely dominated by the likelihood function calculation which now becomes the main bottleneck for increasing computation speed.

14 pages, 2 figures

References in corpus (27)

• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• Planck 2018 results. X. Constraints on inflation
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Planck 2018 results. V. CMB power spectra and likelihoods
• Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code
• Planck 2018 results. VIII. Gravitational lensing
• Cobaya: Code for Bayesian Analysis of hierarchical physical models
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• How many cosmological parameters?
• The Best Inflationary Models After Planck
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• Nested sampling for physical scientists
• Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
• New constraint on Early Dark Energy from Planck and BOSS data using the profile likelihood
• CONNECT: A neural network based framework for emulating cosmological observables and cosmological parameter inference
• CosmicNet II: Emulating extended cosmologies with efficient and accurate neural networks
• Cosmic Inflation at the Crossroads
• Capse.jl: efficient and auto-differentiable CMB power spectra emulation
• Fast Bayesian inference for slow-roll inflation
• Fast and robust Bayesian Inference using Gaussian Processes with GPry
• The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison
• Fast and effortless computation of profile likelihoods using CONNECT
• Uncertainty-aware and Data-efficient Cosmological Emulation using Gaussian Processes and PCA
• Procoli: Profiles of cosmological likelihoods

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