Analytic Methods for Cosmological Likelihoods
  We present general, analytic methods for Cosmological likelihood analysis and
solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's
Method, while marginalization over nuisance parameters, and parameter errors
and covariances are estimated by analytic marginalization of an arbitrary
likelihood function with flat or Gaussian priors. We show that information
about remaining parameters is preserved by marginalization. Marginalizing over
all parameters, we find an analytic expression for the Bayesian evidence for
model selection. We apply these methods to data described by Gaussian
likelihoods with parameters in the mean and covariance. This method can speed
up conventional likelihood analysis by orders of magnitude when combined with
Monte-Carlo Markov Chain methods, while Bayesian model selection becomes
effectively instantaneous.
