Chih-Yuan Tseng, Ariel Caticha
Published 2002-12-09, updated 2002-12-14Version 4
Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first problem. Here we explore its use to tackle the second problem. We show how this use of maximum entropy leads to the Bogoliuvob variational principle which we generalize, apply to density functional theory, and use it to develop a mean field theory for classical fluids. Numerical calculations for Argon gas are compared with experimental data.
Comments: Correctly included 4 figures into the article. Presented at MaxEnt 2002, the 22th International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-7, 2002, Moscow, Idaho, USA)
Journal: p. 73 in "Bayesian Inference and Maximum Entropy Methods in Science and Engineering" ed. by C. J. Williams (A.I.P. Vol. 659, 2003)
Maximum entropy approach to the theory of simple fluids
Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation
Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems
