2017/10/24 by Steen Hannestad, Hannestad, Steen, Thomas Tram +1 · 10 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Bayesian inference #Bayesian linear regression #Bayesian probability #Computer science #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #Estimator #FOS: Physical sciences #Gaussian #Gibbs sampling #Inference #Mathematics #Multivariate normal distribution #Multivariate statistics #Neutrino Physics Research #Parameter space #Particle physics theoretical and experimental studies #Physics #Posterior probability #Prior probability #Statistics #astro-ph.CO
paper · pdf · doi:10.48550/arxiv.1710.08899
published in arXiv (Cornell University) (Cornell University) · As it was pointed out in 1802.09450 and later in 1902.07667, the Jeffreys prior is unchanged by restricting a parameter based on physical considerations. This breaks our assumption of a truncated Gaussian in Eq. 2.10 and thus invalidates our conclusions. (In situations where Eq. 2.10 is a good model of the data, the calculation may still be useful.)
openalex publication_date 2017/10/24 · arxiv created 2019/02/22 · arxiv updated 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is completely determined by the response of the likelihood to changes in parameters. Under the assumption that the likelihood is a Gaussian distribution, the Jeffreys prior is a constant, i.e. flat. However, if one parameter is constrained by physical considerations, the Gaussian approximation fails and the flat prior is no longer the Jeffreys prior. In this paper we compute the correct Jeffreys prior for a multivariate normal distribution constrained in one dimension, and we apply it to the sum of neutrino masses Σmν and the tensor-to-scalar ratio r. We find that one-dimensional marginalised posteriors for these two parameters change considerably and that the 68% and 95% Bayesian upper limits increase by 9% and 4% respectively for Σmν and 22% and 3% for r. Adding the prior to an existing chain can be done as a trivial importance sampling in the final step of the analysis proces.