Measuring the effective complexity of cosmological models

Abstract

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.

9 pages, 4 figures, revised version accepted for publication in PRD, updated with WMAP3 results

References in corpus (11)

• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• How many cosmological parameters?
• The foundations of observing dark energy dynamics with the Wilkinson Microwave Anisotropy Probe
• The essence of quintessence and the cost of compression
• Efficient Cosmological Parameter Estimation from Microwave Background Anisotropies
• Bayesian model selection and isocurvature perturbations
• Constraints on a mixed inflaton and curvaton scenario for the generation of the curvature perturbation
• Revealing the Nature of Dark Energy Using Bayesian Evidence
• Large-scale power in the CMB and new physics: an analysis using Bayesian model comparison
• Constraining topology in harmonic space
• Normal Parameters for an Analytic Description of the CMB Cosmological Parameter Likelihood

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