Calibrating Bayesian Tension Statistics using Neural Ratio Estimation

TL;DR

This paper introduces a neural ratio estimation method to calibrate Bayesian tension metrics, like the evidence ratio, improving their reliability in cosmological data analysis.

Contribution

It presents a novel calibration technique for Bayesian tension metrics using neural ratio estimation, addressing prior dependence issues.

Findings

Effective calibration of evidence ratio R demonstrated

No significant tension found between DESI and SDSS datasets

Method validated with analytic and cosmological examples

Abstract

When fits of the same physical model to two different datasets disagree, we call this tension. Several apparent tensions in cosmology have occupied researchers in recent years, and a number of different metrics have been proposed to quantify tension. Many of these metrics suffer from limiting assumptions, and correctly calibrating these is essential if we want to successfully determine whether discrepancies are significant. A commonly used metric of tension is the evidence ratio R. The statistic has been widely adopted by the community as a Bayesian way of quantifying tensions, however, it has a non-trivial dependence on the prior that is not always accounted for properly. We show that this can be calibrated out effectively with Neural Ratio Estimation. We demonstrate our proposed calibration technique with an analytic example, a toy example inspired by 21-cm cosmology, and with observations of the Baryon Acoustic Oscillations from the Dark Energy Spectroscopic Instrument (DESI) and the Sloan Digital Sky Survey (SDSS). We find no significant tension between DESI and SDSS.