[en] It is well known that the true values of measured and computed data are impossible to know exactly because of various uncontrollable errors and uncertainties arising in the data measurement and interpretation reduction processes. Hence, all inferences, predictions, engineering computations, and other applications of measured and/or computed data are necessarily based on weighted averages over the possibly true values, with weights indicating the degree of plausibility of each value. Furthermore, combination of data from different sources involves a weighted propagation (e.g., via sensitivities) of all uncertainties, requiring reasoning from incomplete information and using probability theory for extracting optimal values together with 'best-estimate' uncertainties from often sparse, incomplete, error-afflicted, and occasionally discrepant data. The current state-of-the-art data assimilation/model calibration methodologies1 for large-scale nonlinear systems cannot take into account uncertainties higher-order than secondorder (i.e., covariances) thereby failing to quantify fully the deviations of the problem under consideration from a normal (Gaussian) multivariate distribution. Such deviations would be quantified by the third- and fourth-order moments (skewness and kurtosis) of the model's predicted results (responses). These higher-order moments would be constructed by combining modeling and experimental uncertainties (which also incorporate the corresponding skewness and kurtosis information), using derivatives of the model responses with respect to the model's parameters. This paper presents explicit expressions for skewness and kurtosis of computed responses, thereby permitting quantification of the deviations of the computed response uncertainties from multivariate normality. In addition, this paper presents a new and most efficient procedure for computing the second-order response derivatives with respect to model parameters using the 'adjoint sensitivity analysis procedure' (ASAP)