On ANOVA expansions and strategies for choosing the anchor point (Q613264)

The analysis-of-variation (ANOVA) expansion provides a way to present functions depending on a high-dimensional variable \(\alpha \in [0,1]^p\). The anchored ANOVA expansion does not require high-dimensional integrations, but its accuracy depends sensitively on the choice of a so-called anchor point. The authors propose that an optimal choice of this anchor point is the center point of a sparse grid quadrature. This approach is based on the structure of the sparse grid of \textit{S. A. Smolyak} [Dokl. Akad. Nauk SSSR 148, 1042--1045 (1963; Zbl 0202.39901)]. Finally, the anchored ANOVA expansion is applied to the high-dimensional integration of test functions.