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

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

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)+

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

Determinants of food availability and access in Ghana: what can we learn beyond the regression results?

The study analyses the determinants of food availability and access, and the causes of unsustainable food access in Ghana using three models. Regression results show that the effects of energy price, domestic and foreign interest rates, domestic prices and exchange rate on food availability are negative, while the effects of crop yield, arable land, liberalisation of agricultural trade and real income are positive. The analysis further shows the unique effects of energy price and human capital exceed their common effects. However, the common effects of domestic and foreign interest rates, inflation, crop yield, arable land, exchange rate, liberalisation of agricultural trade and income exceed their unique effects. The access model shows that the effects of domestic interest rate, exchange rate and oil price are negative. The unique effect of oil price exceeds the variable’s common effect. However, the common effects of exchange rate, interest rate and income exceed their unique effects. The stability model shows that good news and higher incomes enhance sustainable food access. However, higher oil price and depreciation of the local currency distort sustainable food access. The policy implication is that government should jointly target variables with higher common effects when addressing food access and availability. Withdrawal of government fuel subsidy will increase consumers’ risk of accessing food and hence threaten the sustainability of food access