Information geometry in cosmological inference problems

• Verfasst von: Giesel, Eileen [VerfasserIn]
• Verfasst von: Reischke, Robert [VerfasserIn]
• Verfasst von: Schäfer, Björn Malte [VerfasserIn]
• Verfasst von: Chia, Dominic [VerfasserIn]
• Titel: Information geometry in cosmological inference problems
• Verf.angabe: Eileen Giesel, Robert Reischke, Björn Malte Schäfer, Dominic Chia
• E-Jahr: 2021
• Jahr: 4 January 2021
• Umfang: 20 S.
• Teil: year:2021
• Teil: number:1
• Teil: elocationid:005
• Teil: pages:1-20
• Teil: extent:20
• Fussnoten: Gesehen am 11.10.2021
• Titel Quelle: Enthalten in: Journal of cosmology and astroparticle physics
• Ort Quelle: London : IOP, 2003
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), 1, Artikel-ID 005, Seite 1-20
• ISSN Quelle: 1475-7516
• DOI: doi:10.1088/1475-7516/2021/01/005
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1773297120

Abstract

Statistical inference often involves models which are non-linear in the parameters and which therefore typically exhibit non-Gaussian posterior distributions. These non-Gaussianities can be prominent especially when data is limited or not constraining enough. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and empirical Gaussianisation transforms can be constructed that can reduce the amount of non-Gaussianity in a distribution. In this work, we employ methods from information geometry, which considers a set of probability distributions for some given model to be a manifold with a metric Riemannian structure, given by the Fisher information. In this framework we study the differential geometrical meaning of non-Gaussianities in a higher order Fisher approximation, and their respective transformation behaviour under re-parameterisation, which corresponds to a chart transition on the statistical manifold. While weak non-Gaussianities vanish in normal coordinates in a first order approximation, one can in general not find transformations that discard non-Gaussianities globally. As a topical application in cosmology we consider the likelihood of the supernovae distance-redshift relation for the parameter pair (Ωm0, w). We show that the corresponding manifold is non-flat and demonstrate the connection between confidence intervals and geodesic length, determine the curvature of that likelihood and quantify degeneracies by means of Lie-derivatives.