Computational aspects of probabilistic extensions

Abstract

In this article we propose a new approach to computing of functions with random arguments. Approach based on the idea of dimension reduction by to calculating some integrals and the application of numerical probability analysis. We apply one of the basic concepts of numerical probabilistic analysis as the probabilistic extension to computing a function with random arguments. To implement this technique, a new method based on parallel recursive calculations is proposed. Numerical examples are presented demonstrating the effectiveness of the proposed approach.

The Reliability of Numerical Modeling in Remote Sensing Data Analysis

“…We also have proposed the arithmetic operations on probability density functions and procedures for constructing probabilistic extensions as the basis of computational probabilistic analysis [3][4][5][6][7][8][9].…”

“…Thus, the accuracy of addition of n uniform random variables (m = 10) is achieved by Monte Carlo methods with the number of generate uniform random variables equal to n · 10 6 . In the case of dependent random variables, according to 1 and [9], the number of operations increases as m n .…”

Computational Probabilistic Analysis and Transformation Method in the Earth Remote Research

“…Relatively k ∈ R m , we will assume that the probability density functions are known. We will consider the case m ≥ n. Note that the case of strict inequality m > n can be reduced to the case m = n of using the results of probabilistic extensions [8]. Let's consider a special case m = n. Differentiating the original system of nonlinear equations, we obtain…”