@Article{CiCP-9-3,
author = {},
title = {Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {3},
pages = {542--567},
abstract = {<p style="text-align: justify;">The stochastic collocation method using sparse grids has become a popular
choice for performing stochastic computations in high dimensional (random) parameter
space. In addition to providing highly accurate stochastic solutions, the sparse grid
collocation results naturally contain sensitivity information with respect to the input
random parameters. In this paper, we use the sparse grid interpolation and cubature
methods of Smolyak together with combinatorial analysis to give a computationally
efficient method for computing the global sensitivity values of Sobol&#39;. This method allows
for approximation of all <em>main effect</em> and <em>total effect</em> values from evaluation of <em>f </em>on
a single set of sparse grids. We discuss convergence of this method, apply it to several
test cases and compare to existing methods. As a result which may be of independent
interest, we recover an explicit formula for evaluating a Lagrange basis interpolating
polynomial associated with the Chebyshev extrema. This allows one to manipulate
the sparse grid collocation results in a highly efficient manner.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230909.160310s},
url = {https://global-sci.com/article/80857/variance-based-global-sensitivity-analysis-via-sparse-grid-interpolation-and-cubature}
}