Bayesian evidencedriven likelihood selection for skyaveraged 21cm signal extraction
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 likelihoodfree inference (LFI) paradigm. As a concrete example, we use forward modelled skyaveraged 21cm 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, for example, heteroscedastic radiometric or heavytailed noise. For these nonGaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable skyaveraged 21cm 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.
 Publication:

Publications of the Astronomical Society of Australia
 Pub Date:
 April 2023
 DOI:
 10.1017/pasa.2023.16
 arXiv:
 arXiv:2204.04491
 Bibcode:
 2023PASA...40...16S
 Keywords:

 dark ages;
 reionisation;
 first stars;
 methods: statistical;
 methods: data analysis;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 accepted to PASA