On ANOVA-Type Decompositions of Functions with Non-independent Variables: Sensitivity Analysis

<div> ANOVA decompositions are widely used in uncertainty quantication with interesting properties when the input variables are independent. In this paper, we propose the unique decomposition of complex, computational models evaluated at nonindependent variables, which inherits ANOVA properties. The proposed dependent ANOVA (DANOVA) relies on the minimal, symmetric compositions of models by dependency models. An algorithm is provided for selecting such compositions, and the DANOVA is then used for proposing new sensitivity indices that are interpretable in terms of the percentages of the output variance due to each input and interactions. The main and total indices are exactly the Shapley eects of Gaussian inputs using linear models, but dier from Shapley eects in general. Minimum variance and unbiased estimators of DANOVA components; estimators of such indices; and application to computational, auto-regressive models are provided. </div>