TITLE:
Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties
AUTHORS:
Dan Gabriel Cacuci
KEYWORDS:
Fourth-Order Predictive Modeling, Data Assimilation, Data Adjustment, Uncertainty Quantification, Reduced Predicted Uncertainties
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.4,
October
16,
2023
ABSTRACT: 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 4th-BERRU-PM,
which stands for “fourth-order best-estimate results with reduced
uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular
cases, the results previously predicted by the second-order predictive modeling
methodology 2nd-BERRU-PM,
and vastly generalizes the results produced by extant data assimilation and
data adjustment procedures.