On marginals and profiled posteriors for cosmological parameter estimation

Abstract

With several examples and in an analysis of the Pantheon+ supernova sample we discuss the properties of the marginal posterior distribution versus the profiled posterior distribution -- the profile likelihood in a Bayesian disguise. We investigate whether maximisation, as used for the profiling, or integration, as used for the marginalisation, is more appropriate. To report results we recommend the marginal posterior distribution.