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Abstract:
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The Sobol sensitivity indices are originally introduced under the high dimension model representation (HDMR), assuming all the input variables are independent uniform random variables. The variance-based definitions of Sobol indices are available for analyzing systems with correlated or non-uniform inputs. The existing algorithms for estimating Sobol indices with correlated inputs mostly start with approximating the underlying full model by meta-models with certain type of orthogonality among the decomposition components, which is computationally expensive to implement especially when the number of inputs is large. Within the GLM framework, we derived closed or semi-closed formulas for estimating Sobol indices under several commonly used link functions, assuming the inputs are either independent or multivariate normal. By applying these formulas, we can estimate Sobol indices with much less computing cost for GLMs with larger number of correlated inputs. This also means that we can perform ANVOA-type variance decomposition analysis on data with multicollinearity issue, not only under Gaussian regression but also under other type of GLMs such as Poisson and Logistic regression.
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