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Entropy 2014, 16(11), 6059-6098; doi:10.3390/e16116059

How to Read Probability Distributions as Statements about Process

Department of Ecology & Evolutionary Biology, University of California, Irvine, CA 92697, USA
Received: 22 October 2014 / Revised: 13 November 2014 / Accepted: 14 November 2014 / Published: 18 November 2014
(This article belongs to the Section Statistical Mechanics)
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Abstract

Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale of information, opportunities arise to understand the processes that generate the commonly observed patterns. Probability expressions may be parsed into four components: the dissipation of all information, except the preservation of average values, taken over the measurement scale that relates changes in observed values to changes in information, and the transformation from the underlying scale on which information dissipates to alternative scales on which probability pattern may be expressed. Information invariances set the commonly observed measurement scales and the relations between them. In particular, a measurement scale for information is defined by its invariance to specific transformations of underlying values into measurable outputs. Essentially all common distributions can be understood within this simple framework of information invariance and measurement scale. View Full-Text
Keywords: measurement; maximum entropy; information theory; statistical mechanics; extreme value distributions; neutral theories in biology measurement; maximum entropy; information theory; statistical mechanics; extreme value distributions; neutral theories in biology
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. (CC BY 4.0).

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Frank, S.A. How to Read Probability Distributions as Statements about Process. Entropy 2014, 16, 6059-6098.

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