Since the release of microwave anisotropy data from the Wilkinson Microwave Anisotropy Probe (WMAP, Bennett et al. 2003), it has been widely acknowledged that cosmology has entered a precision era, with many of the key cosmological parameters being determined at the ten percent level or better. By now, a wide range of analyses have been published, uniting this dataset with other cosmological datasets such as galaxy power spectrum information from the Two degree field (2dF) survey or the Sloan Digital Sky Survey (SDSS).
While the various analyses are in broad agreement with one another, typically some differences do arise in the precise constraints, for two reasons. One is that separate analyses often use slightly different data compilations, which of course should lead to differing results, hopefully consistent within the uncertainties. However, further differences arise due to the choice of cosmological model made, usually meaning the number of cosmological parameters allowed to vary. The standard approach thus far has been to first choose the set of parameters to be varied on a fairly ad hoc basis, and then use a likelihood method to find the best-fit model and confidence ranges for those parameters. Some papers analyze several combinations of parameters, primarily with the aim of investigating how the parameter confidence ranges are affected by modifying these assumptions.
So far, however, there have been few attempts to allow the data to determine which combination of parameters gives the preferred fit to the data. This is the statistical problem of model selection, which arises across many branches of science; for example, in studies of medical pathologies, one wishes to know which set of indicators, out of many potential factors, are best suited to predicting patient susceptibility. The emphasis is usually on ensuring the elimination of parameters which play an insufficient role in improving the fit to the data available. A key tool is this area is information criteria, specifically the Akaike information criterion (Akaike 1974) and the Bayesian information criterion (Schwarz 1978). These have led to considerable advances in understanding of statistical inference and its relation to information theory; Akaike's 1974 paper now has over 3000 citations and is the subject of a complete textbook (Sakamoto, Ishiguro & Kitagawa 1986). However, so far they seem to have had minimal application in astronomy - keyword search on the abstracts of the entire astro-ph archive yields only three papers (Mukherjee et al. 1998; Takeuchi 2000; Nakamichi & Morikawa 2003). In this paper I will apply the information criteria to the problem of selection of cosmological parameters.