%0 Journal Article %T Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD) %A Dan Gabriel Cacuci %J American Journal of Computational Mathematics %P 236-266 %@ 2161-1211 %D 2023 %I Scientific Research Publishing %R 10.4236/ajcm.2023.132013 %X This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2^nd-BERRU-PMD. The attribute “2^nd” 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 2^nd-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 2^nd-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. %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=125700