Author(s)

Dan Gabriel Cacuci

Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA.

This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4^th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4^th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2^nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.

Fourth-Order Predictive Modeling, Data Assimilation, Data Adjustment, Uncertainty Quantification, Reduced Predicted Uncertainties

Cacuci, D. (2023) Fourth-Order Predictive Modelling: II. 4^th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties. American Journal of Computational Mathematics, 13, 439-475. doi: 10.4236/ajcm.2023.134025.