Boosting MonteCarlo sampling with a non-Gaussian fit

TL;DR

The paper introduces MonteCarlo Posterior Fit, a method that approximates likelihood functions with a non-Gaussian fit, reducing sampling requirements and improving efficiency in complex MonteCarlo simulations.

Contribution

It presents a novel approach to approximate posterior functions with a non-Gaussian fit, decreasing sampling needs and enhancing MonteCarlo performance.

Findings

Requires an order of magnitude fewer samples for comparable precision

Applicable to supernovae and CMB data analysis

Potentially improves all time-consuming MonteCarlo routines

Abstract

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.