Constraining power of open likelihoods, made prior-independent

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.

6 pages, 3 figures; matches version accepted for publication in EPJC

References in corpus (7)

• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Bayes in the sky: Bayesian inference and model selection in cosmology
• An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Observational systematics and baryon acoustic oscillations in the correlation function
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space
• Impacts of dark energy on weighing neutrinos: mass hierarchies considered
• Cosmology-marginalized approaches in Bayesian model comparison: the neutrino mass as a case study

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