We study quasi–Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of ε depends on ε−1 and the dimension s. Strong tractability means that it does not depend on s and is bounded by a polynomial in ε−1. The least po...

Introduction 1 1. Definition and estimation of Sobol indices 2 1.1. Exact model 2 1.2. Estimation of S 3 2. Asymptotic properties: exact model 4 2.1. Consistency and asymptotic normality 4 2.2. Asymptotic efficiency 6 3. Asymptotic properties: metamodel 8 3.1. Metamodel-based estimation 8 3.2. Consistency and asymptotic normality 8 3.3. Asymptotic efficiency 11 4. Numerical illustrations 12 4.1...

introduction: to write a computational program to calculate the average glandular dose in mammography with rh-rh target-filter and also use it as an accurate and fast method of dose calculation founder different situations. materials and methods: in this research, the sobol-wu parameters are used to write a fortran code for glandular dose calculation in rh-rh target-filter mammograms. the code ...

Sensitivity analysis aims to characterize factors (i.e., model inputs) accounting for the amount of uncertainty in model output. Input factors are usually assumed to be independent, which may lead to incorrect conclusions. In this study, a combined sensitivity analysis approach, composed of the Sobol’ and Importance Measurement (IM) methods, is applied on a pesticide environmental risk indicato...

A new method for approximate solution of mechanics problems is presented that uses a classifier to identify regions in a random heterogeneous material where stress is likely to be highly concentrated under a prescribed set of boundary conditions. The example problem studied is an aggregate of hexagonal grains, each modeled as orthotropic and linear elastic, and subject to uniaxial extension. It...