Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method

We develop a complete convergence theory for the Maximum Entropy method based on moment matching for a sequence of approximate statistical moments estimated by the Multilevel Monte Carlo method. Under appropriate regularity assumptions on the target probability density function, the proposed method is superior to the Maximum Entropy method with moments estimated by the Monte Carlo method. New theoretical results are illustrated in numerical examples. (C) 2016 Elsevier Inc. All rights reserved.