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.
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