Journal
PHYSICAL REVIEW D
Volume 100, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.100.023512
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Funding
- Engineering and Physical Sciences Research Council [EP/P020259/1]
- Science and Technology Facilities Council
- Gonville Caius College
- UCL via a Science and Technology Facilities Council Consolidated Grant
- EPSRC [EP/P020259/1] Funding Source: UKRI
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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.
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