Speaker
Description
Reconstruction of distributions from Monte-Carlo simulations is a standard problem in high-energy physics.
Traditionally, this is done by collecting the generated events in histograms. I will present an alternative approach, the main idea of which is to approximate the target distribution as a sum of orthogonal basis functions with coefficients that are given by certain moments of the target distribution, which are calculated using the Monte-Carlo integration. This method has the advantage of directly yielding smooth approximations to target distributions, and, in the context of perturbative calculations with local subtractions, it protects against so-called bin-to-bin fluctuations, which often severely affect the quality of conventional histograms. I will propose a prescription for truncation of the functional expansion and a method for estimating the Monte-Carlo and truncation errors. I will also discuss how an initial approximation to the target distribution, such as a leading-order result, can be used to construct an orthonormal basis that is optimized for the specific distribution.