Calculating Bayesian evidence for inflationary models using connect

TY - JOUR

T1 - Calculating Bayesian evidence for inflationary models using connect

AU - Sørensen, Camilla T.G.

AU - Hannestad, Steen

AU - Nygaard, Andreas

AU - Tram, Thomas

N1 - Publisher Copyright: © 2025 The Author(s)

PY - 2025/3/1

Y1 - 2025/3/1

N2 - 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 ΛCDM 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 O(106) 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.

AB - 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 ΛCDM 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 O(106) 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.

KW - Bayesian reasoning

KW - Inflation and CMBR theory

KW - Machine learning

KW - Statistical sampling techniques

UR - http://www.scopus.com/inward/record.url?scp=105000521901&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2025/03/043

DO - 10.1088/1475-7516/2025/03/043

M3 - Journal article

AN - SCOPUS:105000521901

SN - 1475-7516

VL - 2025

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 3

M1 - 043

ER -