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Entropy 2014, 16(7), 4004-4014; doi:10.3390/e16074004

A Note of Caution on Maximizing Entropy

1,*  and 2
1 Department of Preventive Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA 2 Department of Biomedical Informatics, University of Pittsburgh, Pittsburgh, PA 15232, USA
* Author to whom correspondence should be addressed.
Received: 4 May 2014 / Revised: 10 July 2014 / Accepted: 15 July 2014 / Published: 17 July 2014
(This article belongs to the Special Issue Maximum Entropy and Its Application)
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The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
Keywords: maximum entropy; classical approach; limiting frequency; Bayesian; subjective probability maximum entropy; classical approach; limiting frequency; Bayesian; subjective probability
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Neapolitan, R.E.; Jiang, X. A Note of Caution on Maximizing Entropy. Entropy 2014, 16, 4004-4014.

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