  We propose a new method, called MonteCarlo Posterior Fit, to boost the
MonteCarlo sampling of likelihood (posterior) functions. The idea is to
approximate the posterior function by an analytical multidimensional
non-Gaussian fit. The many free parameters of this fit can be obtained by a
smaller sampling than is needed to derive the full numerical posterior. In the
examples that we consider, based on supernovae and cosmic microwave background
data, we find that one needs an order of magnitude smaller sampling than in the
standard algorithms to achieve comparable precision. This method can be applied
to a variety of situations and is expected to significantly improve the
performance of the MonteCarlo routines in all the cases in which sampling is
very time-consuming. Finally, it can also be applied to Fisher matrix
forecasts, and can help solve various limitations of the standard approach.
