  Constraints on cosmological parameters depend on the set of parameters chosen
to define the model which is compared with observational data. I use the Akaike
and Bayesian information criteria to carry out cosmological model selection, in
order to determine the parameter set providing the preferred fit to the data.
Applying the information criteria to the current cosmological data sets
indicates, for example, that spatially-flat models are statistically preferred
to closed models, and that possible running of the spectral index has lower
significance than inferred from its confidence limits. I also discuss some
problems of statistical assessment arising from there being a large number of
`candidate' cosmological parameters that can be investigated for possible
cosmological implications, and argue that 95% confidence is too low a threshold
to robustly identify the need for new parameters in model fitting. The best
present description of cosmological data uses a scale-invariant (n=1) spectrum
of gaussian adiabatic perturbations in a spatially-flat Universe, with the
cosmological model requiring only five fundamental parameters to fully specify
it.

Astrophysics