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Entropy 2014, 16(2), 1123-1133; doi:10.3390/e16021123
Article

A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean

1,*  and 1,2
Received: 16 December 2013; in revised form: 11 February 2014 / Accepted: 13 February 2014 / Published: 24 February 2014
(This article belongs to the Special Issue Maximum Entropy and Its Application)
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Abstract: There are two entropy-based methods to deal with linear inverse problems, which we shall call the ordinary method of maximum entropy (OME) and the method of maximum entropy in the mean (MEM). Not only doesMEM use OME as a stepping stone, it also allows for greater generality. First, because it allows to include convex constraints in a natural way, and second, because it allows to incorporate and to estimate (additive) measurement errors from the data. Here we shall see both methods in action in a specific example. We shall solve the discretized version of the problem by two variants of MEM and directly with OME. We shall see that OME is actually a particular instance of MEM, when the reference measure is a Poisson Measure.
Keywords: maximum entropy; maximum entropy in the mean; constrained linear inverse problems maximum entropy; maximum entropy in the mean; constrained linear inverse problems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Gzyl, H.; ter Horst, E. A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean. Entropy 2014, 16, 1123-1133.

AMA Style

Gzyl H, ter Horst E. A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean. Entropy. 2014; 16(2):1123-1133.

Chicago/Turabian Style

Gzyl, Henryk; ter Horst, Enrique. 2014. "A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean." Entropy 16, no. 2: 1123-1133.


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