A Maximum Entropy Moment Closure Approach to Describing Spray Flows

1998 ◽  
Author(s):  
M. Archambault ◽  
R. W. MacCormack ◽  
C. F. Edwards
Keyword(s):  
Maximum Entropy ◽  
Moment Closure ◽  
Spray Flows

scholarly journals Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

2010 ◽  
Vol 138 (8) ◽  
pp. 2997-3023 ◽  
Author(s):  
Marc Bocquet ◽  
Carlos A. Pires ◽  
Lin Wu
Keyword(s):  
Data Assimilation ◽  
Maximum Entropy ◽  
Statistical Modeling ◽  
Estimation Problem ◽  
Geophysical Data ◽  
Moment Closure ◽  
High Dimensional ◽  
Order Moment ◽  
Special Cases ◽  
Non Gaussian

Abstract This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.

Multi-dimensional validation of a maximum-entropy-based interpolative moment closure

2016 ◽  
Author(s):  
Boone R. Tensuda ◽  
James G. McDonald ◽  
Clinton P. T. Groth
Keyword(s):  
Maximum Entropy ◽  
Moment Closure

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Predicting Job Performance in Small Samples using the Generalized Maximum Entropy Formulation

2012 ◽  
Author(s):  
Pedro J. Ramos-Villagrasa ◽  
Blanca Moreno ◽  
Antonio L. Garcie-Izquierdo
Keyword(s):  
Job Performance ◽  
Maximum Entropy ◽  
Small Samples ◽  
Generalized Maximum Entropy ◽  
Entropy Formulation
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