Principle of maximum entropy

The maximum entropy method or MEM is a method of Bayesian statistics, which allows you to assign an a priori probability in spite of defective problem-specific information. It replaces previous approaches such as the Laplace formulated " principle of insufficient reason ".

Origin and Procedure

The method was introduced in 1957 by Edwin Thompson Jaynes based on methods of statistical mechanics and Shannon information theory. It is based on maximizing the entropy information in the absence of the a priori probability that any other assignment would meet arbitrary restrictions on the situation under consideration. The maximum entropy method commits himself as little as possible. But according to Jaynes, this is only the last step to any after filling all available information to close remaining gaps.

In statistical physics, this means: " Among all the states of a physical system that are compatible with the existing knowledge about the system that is to be chosen which maximizes the entropy. "

The method is used for optimum extraction of information from the noisy signal as a function of the signal -to-noise ratio. It takes place in the spectral analysis and digital image processing application.

Applications in economics

A relatively new area of ​​application of the MEM, the macroeconomics dar. Under the ökonophysikalischen flow that applies different methods of statistical mechanics to the modeling of the economy away from the economics mainstream, it came to the use of the MEM.

Applications in ecology

In biogeography, the maximum entropy method for modeling distribution areas is used. One example is the software Maxent.