On marginals and profiled posteriors for cosmological parameter estimation

TL;DR

This paper compares marginal and profiled posterior distributions in cosmological parameter estimation, advocating for the use of marginal posteriors based on analysis of supernova data.

Contribution

It provides a detailed analysis of the properties of marginal versus profiled posteriors and recommends marginal posteriors for reporting results in cosmology.

Findings

Marginal posteriors better represent parameter uncertainties.

Profiling can lead to biased or less informative results.

Analysis of Pantheon+ supernova data supports marginalization as preferable.

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.