TITLE:
Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)
AUTHORS:
Dan Gabriel Cacuci
KEYWORDS:
Second-Order Predictive Modeling, Data Assimilation, Data Adjustment, Uncertainty Quantification, Reduced Predicted Uncertainties
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.2,
June
20,
2023
ABSTRACT: This work presents a comprehensive second-order
predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD.
The attribute “2nd” indicates that this methodology incorporates
second-order uncertainties (means and covariances) and second-order
sensitivities of computed model responses to
model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”)
in the acronym indicates “deterministic,” referring to the deterministic
inclusion of the computational model responses. The 2nd-BERRU-PMD
methodology is fundamentally based on the maximum entropy (MaxEnt) principle.
This principle is in contradistinction to the fundamental principle that
underlies the extant data assimilation and/or adjustment
procedures which minimize in a least-square sense a subjective user-defined
functional which is meant to represent the discrepancies between measured and
computed model responses. It is shown that the 2nd-BERRU-PMD
methodology generalizes and extends current data assimilation and/or data
adjustment procedures while overcoming the fundamental limitations of these
procedures. In the accompanying work (Part II), the alternative framework for
developing the “second- order MaxEnt predictive modelling methodology” is presented by
incorporating probabilistically (as opposed to “deterministically”) the
computed model responses.