  Bayesian model selection is a tool to decide whether the introduction of a
new parameter is warranted by data. I argue that the usual sampling statistic
significance tests for a null hypothesis can be misleading, since they do not
take into account the information gained through the data, when updating the
prior distribution to the posterior. On the contrary, Bayesian model selection
offers a quantitative implementation of Occam's razor.
  I introduce the Savage-Dickey density ratio, a computationally quick method
to determine the Bayes factor of two nested models and hence perform model
selection. As an illustration, I consider three key parameters for our
understanding of the cosmological concordance model. By using WMAP 3-year data
complemented by other cosmological measurements, I show that a non-scale
invariant spectral index of perturbations is favoured for any sensible choice
of prior. It is also found that a flat Universe is favoured with odds of 29:1
over non--flat models, and that there is strong evidence against a CDM
isocurvature component to the initial conditions which is totally
(anti)correlated with the adiabatic mode (odds of about 2000:1), but that this
is strongly dependent on the prior adopted.
  These results are contrasted with the analysis of WMAP 1-year data, which
were not informative enough to allow a conclusion as to the status of the
spectral index. In a companion paper, a new technique to forecast the Bayes
factor of a future observation is presented.
