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Entropy 2015, 17(11), 7453-7467; doi:10.3390/e17117453

Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA
Academic Editor: Takuya Yamano
Received: 11 September 2015 / Accepted: 11 October 2015 / Published: 28 October 2015
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
View Full-Text   |   Download PDF [196 KB, uploaded 28 October 2015]

Abstract

Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described. View Full-Text
Keywords: Fisher information; extreme physical information; EPI; EPI derived; epistemology; coarse graining; Kullback–Leibler entropy; Plato’s cave; transition from substance to information; cancer growth Fisher information; extreme physical information; EPI; EPI derived; epistemology; coarse graining; Kullback–Leibler entropy; Plato’s cave; transition from substance to information; cancer growth
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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Frieden, B.R. Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation. Entropy 2015, 17, 7453-7467.

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