Open AccessInformation criteria for astrophysical model selection
Author(s) -
Liddle Andrew R.
Publication year - 2007
Publication title -
monthly notices of the royal astronomical society: letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.067
H-Index - 122
eISSN - 1745-3933
pISSN - 1745-3925
DOI - 10.1111/j.1745-3933.2007.00306.x
Subject(s) - akaike information criterion , deviance information criterion , bayesian information criterion , information criteria , model selection , bayesian probability , bayesian inference , bayesian experimental design , computer science , deviance (statistics) , information theory , bayesian average , bayesian statistics , statistics , mathematics , econometrics , machine learning , artificial intelligence
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 Wilkinson Microwave Anisotropy Probe 3‐yr data for several cosmological models. I find that at present the information theory and Bayesian approaches give significantly different conclusions from that data.