49 research outputs found
Approximation for a Toy Defective Ising Model
It has been previously shown that one can use the ME methodology (Caticha
Giffin 2006) to reproduce a mean field solution for a simple fluid (Tseng
2004). One could easily use the case of a simple ferromagnetic material as
well. The drawback to the mean field approach is that one must assume that all
atoms must all act the same. The problem becomes more tractable when the agents
are only allowed to interact with their nearest neighbors and can be in only
two possible states. The easiest case being an Ising model. The purpose of this
paper is to illustrate the use of the ME method as an approximation tool. The
paper show a simple case to compare with the traditional mean field approach.
Then we show two examples that lie outside of traditional methodologies. These
cases explore a ferromagnetic material with defects. The main result is that
regardless of the case, the ME method provides good approximations for each
case which would not otherwise be possible or at least well justified.Comment: Presented at the 29th International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Oxford, MS, July
5-10, 2009. 10 pages, 0 figure
Updating Probabilities
We show that Skilling's method of induction leads to a unique general theory
of inductive inference, the method of Maximum relative Entropy (ME). The main
tool for updating probabilities is the logarithmic relative entropy; other
entropies such as those of Renyi or Tsallis are ruled out. We also show that
Bayes updating is a special case of ME updating and thus, that the two are
completely compatible.Comment: Presented at MaxEnt 2006, the 26th International Workshop on Bayesian
Inference and Maximum Entropy Methods (July 8-13, 2006, Paris, France
Updating Probabilities with Data and Moments
We use the method of Maximum (relative) Entropy to process information in the
form of observed data and moment constraints. The generic "canonical" form of
the posterior distribution for the problem of simultaneous updating with data
and moments is obtained. We discuss the general problem of non-commuting
constraints, when they should be processed sequentially and when
simultaneously. As an illustration, the multinomial example of die tosses is
solved in detail for two superficially similar but actually very different
problems.Comment: Presented at the 27th International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Saratoga Springs, NY,
July 8-13, 2007. 10 pages, 1 figure V2 has a small typo in the end of the
appendix that was fixed. aj=mj+1 is now aj=m(k-j)+
From Physics to Economics: An Econometric Example Using Maximum Relative Entropy
Econophysics, is based on the premise that some ideas and methods from
physics can be applied to economic situations. We intend to show in this paper
how a physics concept such as entropy can be applied to an economic problem. In
so doing, we demonstrate how information in the form of observable data and
moment constraints are introduced into the method of Maximum relative Entropy
(MrE). A general example of updating with data and moments is shown. Two
specific econometric examples are solved in detail which can then be used as
templates for real world problems. A numerical example is compared to a large
deviation solution which illustrates some of the advantages of the MrE method.Comment: This paper has been accepted in Physica A. 19 Pages, 3 Figure
An Application of Reversible Entropic Dynamics on Curved Statistical Manifolds
Entropic Dynamics (ED) is a theoretical framework developed to investigate
the possibility that laws of physics reflect laws of inference rather than laws
of nature. In this work, a RED (Reversible Entropic Dynamics) model is
considered. The geometric structure underlying the curved statistical manifold,
M is studied. The trajectories of this particular model are hyperbolic curves
(geodesics) on M. Finally, some analysis concerning the stability of these
geodesics on M is carried out.Comment: Presented at MaxEnt 2006, the 26th International Workshop on Bayesian
Inference and Maximum Entropy Methods (July 8-13, 2006, Paris, France). This
paper is slightly updated from the published version. This paper consists of
9 pages with 1 figure. Keywords: Inductive inference, information geometry,
statistical manifolds, relative entrop