Technical Note—A Generalized Maximum Entropy Principle

Abstract

We describe a generalized maximum entropy principle for dealing with decision problems involving uncertainty but with some prior knowledge about the probability space corresponding to nature. This knowledge is expressed through known bounds on event probabilities and moments, which can be incorporated into a nonlinear programming problem. The solution provides a maximum entropy distribution that is then used in treating the decision problem as one involving risk. We describe an example application that involves the selection of oil spill recovery systems for inland harbor regions.

The evolving concept of air pollution: a small‐world network or scale‐free network?

“…Therefore, air pollution index fluctuations obey an index distribution, and this law is similar to the distribution of the number of times that all types of earthquakes occur in the earth system (Abe and Suzuki, ). The reason may be that the pollution process follows the maximum entropy principle (Thomas, ), which embodies the inherent essential dynamic characteristics of the atmosphere system to a certain extent.…”

Modeling and Optimization of Risk

“…Entropy maximization is a fundamental principle originated from the information theory and statistical mechanics (see Jaynes (1957)) and finds its application in financial engineering and decision making under risk (Cozzolino and Zahner, 1973;Thomas, 1979;Buckley, 1979). The principle determines the least-informative (or most unbiased) probability distribution for a random variable X given some prior information about X.…”

The effectiveness of imprecise probability forecasts

“…Thomas, 1979). As explained in detail later, the formulation was accomplished in the present study by requiring subjects to assess (1) the prior, p and (2) probability intervals for each of the elements in q.…”

“…Areas of application include business and economics, behavioral sciences, engineering, law, and risk assessment (cf. Cozzolino and Zahner, 1973; Kapur, 1982; Thomas, 1979; Smith, 1979,1982).…”