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.
In the particular case of sensitivity analysis using conventional methods, the number of large-scale computations increases exponentially. For large-scale models involving many parameters, even the first-order sensitivities are computationally very expensive to determine accurately by conventional methods. Furthermore, the “curse of dimensionality” prohibits the accurate computation of higher-order sensitivities by conventional methods.
Other books by the author, all published by CRC Press, include Sensitivity and Uncertainty Analysis, Volume I: Theory (2003); Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems (Cacuci, et al., 2005); Computational Methods for Data Evaluation and Assimilation (Cacuci et al. 2014); The Second-Order Adjoint Sensitivity Analysis Methodology (2018); and Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems (2025).