Boosting Monte Carlo sampling with a non-Gaussian fit

We propose a new method, called Monte Carlo Posterior Fit, to boost the Monte Carlo 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 Monte Carlo 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.