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Quantifying dimensionality: Bayesian cosmological model complexities

Handley, W; Lemos, P; (2019) Quantifying dimensionality: Bayesian cosmological model complexities. Physical Review D , 100 (2) , Article 023512. 10.1103/PhysRevD.100.023512. Green open access

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Abstract

We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e., the Kullback-Leibler divergence) provides a measure of the strength of constraint between prior and posterior, we show that the variance of the Shannon information gives a measure of dimensionality of constraint. We examine this quantity in a cosmological context, applying it to likelihoods derived from the cosmic microwave background, large-scale structure and supernovae data. We show that this measure of Bayesian model dimensionality compares favorably both analytically and numerically in a cosmological context with the existing measure of model complexity used in the literature.

Type: Article
Title: Quantifying dimensionality: Bayesian cosmological model complexities
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevD.100.023512
Publisher version: https://doi.org/10.1103/PhysRevD.100.023512
Language: English
Additional information: This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: http://discovery.ucl.ac.uk/id/eprint/10078669
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