We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function \(f:\mathbb {S}^d\rightarrow \mathbb {R}\) into a sum of terms \(f_{\varvec{u},\varvec{\xi }}\) . The index \(\varvec{u}\) is a subset of \(\{1,2,\ldots ,d+1\}\) , where each term \(f_{\varvec{u},\varvec{\xi }}\) depends only on the variables with indices in \(\varvec{u}\) . In contrast to the classical analysis of variance (ANOVA) decomposition, we additionally use the decomposition of a function into functions with different parity, which adds the additional parameter \(\varvec{\xi }\) . The natural geometry on the sphere naturally leads to the dependencies between the input variables. Using certain orthogonal basis functions for the function approximation, we are able to model high-dimensional functions with low-dimensional variable interactions.
