  Model selection aims to determine which theoretical models are most plausible
given some data, without necessarily asking about the preferred values of the
model parameters. A common model selection question is to ask when new data
require introduction of an additional parameter, describing a newly-discovered
physical effect. We review several model selection statistics, and then focus
on use of the Bayesian evidence, which implements the usual Bayesian analysis
framework at the level of models rather than parameters. We describe our
CosmoNest code, which is the first computationally-efficient implementation of
Bayesian model selection in a cosmological context. We apply it to recent WMAP
satellite data, examining the need for a perturbation spectral index differing
from the scale-invariant (Harrison-Zel'dovich) case.
