%0 Journal Article
%T Fourth-Order Predictive Modelling: II. 4<sup>th</sup>-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties
%A Dan Gabriel Cacuci
%J American Journal of Computational Mathematics
%P 439-475
%@ 2161-1211
%D 2023
%I Scientific Research Publishing
%R 10.4236/ajcm.2023.134025
%X <span style=\"font-family:;\" \"=\"\"><span style=\"font-family:Verdana;\">This work presents a comprehensive fourth-order
predictive modeling (PM) </span><span style=\"font-family:Verdana;\">methodology that
uses the MaxEnt principle to incorporate fourth-order moments (means,
covariances, skewness, kurtosis) of model parameter</span><span style=\"font-family:Verdana;\">s, 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 </span><span><span style=\"font-family:Verdana;\">4</span><i><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-BERRU-PM</span></i></span><span style=\"font-family:Verdana;\">,
which stands for ˇ°fourth-order best-estimate results with reduced
uncertainties.ˇ± The results predicted by the </span><span><span style=\"font-family:Verdana;\">4</span><i><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-BERRU-PM</span></i></span><span style=\"font-family:Verdana;\"> incorporates, as particular
cases, the results previously predicted by the second-order predictive modeling
methodology </span><span><span style=\"font-family:Verdana;\">2</span><i><sup><span style=\"font-family:Verdana;\">nd</span></sup><span style=\"font-family:Verdana;\">-BERRU-PM</span></i></span><span style=\"font-family:Verdana;\">,
and vastly generalizes the results produced by extant data assimilation and
data adjustment procedures.</span></span>
%K Fourth-Order Predictive Modeling
%K Data Assimilation
%K Data Adjustment
%K Uncertainty Quantification
%K Reduced Predicted Uncertainties
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=128315