Bayesian evidence-driven likelihood selection for sky-averaged 21-cm
  signal extraction
  We demonstrate that the Bayesian evidence can be used to find a good
approximation of the true 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 true 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.
