Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)
Dan Gabriel Cacuci
Abstract
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 "secondorder MaxEnt predictive modelling methodology" is presented by incorporating probabilistically (as opposed to "deterministically") the computed model responses.