%0 Journal Article
%T Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution
%A Dan Gabriel Cacuci
%J American Journal of Computational Mathematics
%P 413-438
%@ 2161-1211
%D 2023
%I Scientific Research Publishing
%R 10.4236/ajcm.2023.134024
%X <span style=\"font-family:Verdana;\">This work (in two parts) will present a novel
predictive modeling methodology aimed at obtaining ˇ°best-estimate results with
reduced uncertaintiesˇ± for the first four moments (mean values, covariance,
skewness and kurtosis) of the optimally predicted distribution of model results
and calibrated model parameters, by combining fourth-order experimental and
computational information, including fourth (and higher) order sensitivities of
computed mo</span><span style=\"font-family:Verdana;\">del responses to model
parameters. Underlying the construction of this fourth-order predictive
modeling methodology is the ˇ°maximum entro</span><span style=\"font-family:Verdana;\">py principleˇ± which is
initially used to obtain a novel closed-form expression of </span><span style=\"font-family:Verdana;\">the (moments-constrained) fourth-order Maximum
Entropy (MaxEnt)</span><span style=\"font-family:Verdana;\"> probability </span><span style=\"font-family:Verdana;\">distribution
constructed from the first four moments (means,</span><span style=\"font-family:Verdana;\"> covariances, skewness,
kurtosis), which are assumed to be known, of an otherwise unknown distribution
of a high-dimensional multivariate uncertain quantity of interest. This
fourth-order MaxEnt distribution provides optimal compatibility </span><span style=\"font-family:Verdana;\">of the available information while simultaneously
ensuring minimal spurious information content, yielding an estimate of a
probability density with </span></span><span style=\"font-size:10pt;font-family:Verdana;\">the </span><span style=\"font-size:10pt;font-family:Verdana;\">highest uncertainty among all densities satisfying
the known moment constraints. Since this novel generic fourth-order MaxEnt
distrib</span><span style=\"font-size:10pt;font-family:Verdana;\">ution is of interest in its own right for applications in addition to
predictive modeling, its construction is presented separately, in this first
part of a two-part work. The fourth-order predictive modeling methodology that
will be constructed by particularizing this generic fourth-order MaxEnt
distribution will be presented in the accompanying work (Part-2).
%K Maximum Entropy Principle
%K Fourth-Order Predictive Modeling
%K Data Assimilation
%K Data Adjustment
%K Reduced Predicted Uncertainties
%K Model Parameter Calibration
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=128310