Advances in High-Order Sensitivity Analysis (Advances in Applied Mathematics)

The high-order sensitivities of model responses with respect to model parameters are notoriously difficult to compute for large-scale models involving many parameters.The neglect of higher-order response sensitivities leads to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis, and higher-order) of the model response’s distribution in the phase space of model parameters.The author expands on his theory of addressing high-order sensitivity analysis in this book, Advances in High-Order Sensitivity Analysis. The mathematical/computational models of physical systems comprise parameters, independent variables, and dependent variables.Since the physical processes themselves are seldom known precisely and since most of the model’s parameters stem from experimental procedures that are also subject to imprecision and/or uncertainties, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model