Constraining power of open likelihoods, made prior-independent

TL;DR

This paper presents a prior-independent method for deriving constraints from open likelihoods, addressing a key criticism of Bayesian credible intervals and demonstrating its application to cosmological neutrino mass bounds.

Contribution

The authors revive and extend a simple prior-independent method for constraining parameters, overcoming prior dependence issues in Bayesian analysis, especially for open likelihoods.

Findings

Method yields prior-independent constraints in cosmology

Extension reduces dependence on parameter choices in numerical analysis

Applicable to open likelihood scenarios in Bayesian statistics

Abstract

One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are affected by the eternal dilemma of choosing between linear and logarithmic prior, and in particular in the latter case the situation is worsened by the dependence on the prior range under consideration. In this letter, we revive a simple method to obtain constraints that depend neither on the prior shape nor range and, using the tools of Bayesian model comparison, extend it to overcome the possible dependence of the bounds on the choice of free parameters in the numerical analysis. An application to the case of cosmological bounds on the sum of the neutrino masses is discussed as an example.