Journal Article

The reliability of the Akaike information criterion method in cosmological model selection

M. Y. J. Tan and Rahul Biswas

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 419, issue 4, pages 3292-3303
Published in print February 2012 | ISSN: 0035-8711
Published online January 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19969.x
The reliability of the Akaike information criterion method in cosmological model selection

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The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect estimate of the Kullback–Leibler divergence D(TA) of a candidate model A with respect to the truth T. Thus, a dark energy model with a smaller AIC is ranked as a better model, since it has a smaller Kullback–Leibler discrepancy with T. In this paper, we explore the impact of statistical errors in estimating the AIC during model comparison. Using a parametric bootstrap technique, we study the distribution of AIC differences between a set of candidate models due to different realizations of noise in the data and show that the shape and spread of this distribution can be quite varied. We also study the rate of success of the AIC procedure for different values of a threshold parameter popularly used in the literature. For plausible choices of true dark energy models, our studies suggest that investigating such distributions of AIC differences in addition to the threshold is useful in correctly interpreting comparisons of dark energy models using the AIC technique.

Keywords: methods: data analysis; methods: statistical; cosmology: theory

Journal Article.  9256 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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