Parallel Monte Carlo for entropy robust estimation


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Abstract

A new method of entropy-robust nonparametric estimation of probability density functions (PDFs) of the characteristics of dynamic randomized models with structured nonlinearities given a small amount of data is proposed. Optimal PDFs are shown to belong to the exponential class with Lagrange multipliers being its parameters. In order to determine these parameters, a system of equations with integral components is constructed. An algorithm for solving this problem is developed based on parallel Monte Carlo techniques. The accuracy of the numerical integration for the given class of integral components and the probability of its achievement are estimated. The method is applied to a second-degree nonlinear dynamic system with the given structure of exponential nonlinearity.

About the authors

Yu. S. Popkov

Institute for Systems Analysis; Moscow Institute of Physics and Technology; National Research University Higher School of Economics; Moscow State University

Author for correspondence.
Email: popkov.alexey@gmail.com
Russian Federation, Moscow, 117312; Dolgoprudny, Moscow region, 141700; Moscow, 101000; Moscow, 119899

A. Yu. Popkov

Institute for Systems Analysis

Email: popkov.alexey@gmail.com
Russian Federation, Moscow, 117312

B. S. Darkhovsky

Institute for Systems Analysis; Moscow Institute of Physics and Technology

Email: popkov.alexey@gmail.com
Russian Federation, Moscow, 117312; Dolgoprudny, Moscow region, 141700

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