Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction

TL;DR

This paper shows that Bayesian evidence can guide the selection of an appropriate likelihood function for sky-averaged 21-cm signal analysis, especially when noise deviates from Gaussian, by using the generalized normal distribution as a flexible approximation.

Contribution

It introduces a Bayesian evidence-based method to select likelihood functions, demonstrating the effectiveness of the generalized normal likelihood for non-Gaussian noise in 21-cm signal extraction.

Findings

Gaussian likelihood performs poorly with non-Gaussian noise

Generalized normal likelihood matches the true likelihood in Bayesian evidence

Proposes generalized normal as a robust likelihood approximation

Abstract

We demonstrate that the Bayesian evidence can be used to find a good approximation of the ground truth likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled sky-averaged 21-cm signal antenna temperature datasets where we artificially inject noise structures of various physically motivated forms. We find that the Gaussian likelihood performs poorly when the noise distribution deviates from the Gaussian case e.g. heteroscedastic radiometric or heavy-tailed noise. For these non-Gaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable sky-averaged 21-cm signal recovery as the ground truth likelihood function of our injected noise. We therefore propose the generalised normal likelihood function as a good approximation of the true likelihood function if the noise structure is a priori unknown.