%0 Journal Article
%T Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)
%A Dan Gabriel Cacuci
%J American Journal of Computational Mathematics
%P 267-294
%@ 2161-1211
%D 2023
%I Scientific Research Publishing
%R 10.4236/ajcm.2023.132014
%X This work presents a comprehensive second-order predictive modeling (PM)
methodology based on the maximum entropy (MaxEnt) principle for obtaining
best-estimate mean values and correlations for model responses and parameters.
This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute ¡°2nd¡± indicates
that this methodology incorporates second- order uncertainties
(means and covariances) and second (and higher) order sensitivities of computed
model responses to model parameters. The acronym BERRU stands for
¡°Best-Estimate Results with Reduced Uncertainties¡± and the last letter (¡°P¡±)
in the acronym indicates ¡°probabilistic,¡± referring to the MaxEnt probabilistic
inclusion of the computational model responses. This is in contradistinction to
the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as
presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that
include second (and higher) order sensitivities of responses to model
parameters, the respective expressions for the predicted responses, for the
calibrated predicted parameters and for their predicted uncertainties
(covariances), are not identical to each other. Nevertheless, the results
predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the
extant data assimilation and data adjustment procedures, which rely on the
minimization, in a least-square sense, of a user-defined functional meant to
represent the discrepancies between measured and computed model responses.
%K Second-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=125703