Quantifying dimensionality: Bayesian cosmological model complexities
  We demonstrate a measure for the effective number of parameters constrained
by a posterior distribution in the context of cosmology. In the same way that
the mean of the Shannon information (i.e. the Kullback-Leibler divergence)
provides a measure of the strength of constraint between prior and posterior,
we show that the variance of the Shannon information gives a measure of
dimensionality of constraint. We examine this quantity in a cosmological
context, applying it to likelihoods derived from Cosmic Microwave Background,
large scale structure and supernovae data. We show that this measure of
Bayesian model dimensionality compares favourably both analytically and
numerically in a cosmological context with the existing measure of model
complexity used in the literature.
