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Information criteria for astrophysical model selection

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arxiv astro-ph/0701113 v2 pith:JX2MHP5L submitted 2007-01-04 astro-ph

Information criteria for astrophysical model selection

classification astro-ph
keywords informationbayesiancriterioncriteriadatadifferentmodelmodels
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike Information Criterion (AIC), and those on Bayesian inference such as the Bayesian evidence and Bayesian Information Criterion (BIC). The Deviance Information Criterion combines ideas from both heritages; it is readily computed from Monte Carlo posterior samples and, unlike the AIC and BIC, allows for parameter degeneracy. I describe the properties of the information criteria, and as an example compute them from WMAP3 data for several cosmological models. I find that at present the information theory and Bayesian approaches give significantly different conclusions from that data.

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