Non-Gaussian estimates of tensions in cosmological parameters

TL;DR

This paper introduces scalable algorithms using kernel density estimates and normalizing flows to accurately assess tensions between cosmological parameter measurements, accounting for non-Gaussian posteriors.

Contribution

It presents two novel, scalable methods for estimating tensions in cosmological parameters that handle non-Gaussian posteriors and demonstrate high accuracy.

Findings

Both methods agree within 0.5σ in difficult cases

Methods achieve better than 0.2σ accuracy in general

Applied to compare Dark Energy Survey and Planck data

Abstract

We discuss how to efficiently and reliably estimate the level of agreement and disagreement on parameter determinations from different experiments, fully taking into account non-Gaussianities in the parameter posteriors. We develop two families of scalable algorithms that allow us to perform this type of calculations in increasing number of dimensions and for different levels of tensions. One family of algorithms rely on kernel density estimates of posterior distributions while the other relies on machine learning modeling of the posterior distribution with normalizing flows. We showcase their effectiveness and accuracy with a set of benchmark examples and find both methods agree with each other and the true tension within $0.5\sigma$ in difficult cases and generally to $0.2\sigma$ or better. This allows us to study the level of internal agreement between different measurements of the clustering of cosmological structures from the Dark Energy Survey and their agreement with measurements of the Cosmic Microwave Background from the Planck satellite.