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Entropy 2017, 19(2), 75; doi:10.3390/e19020075

Information Loss in Binomial Data Due to Data Compression

1
Battelle Center for Mathematical Medicine, The Research Institute, Nationwide Children’s Hospital, Columbus, OH 43215, USA
2
Department of Pediatrics, The Ohio State University, Columbus, OH 43210, USA
3
Department of Statistics, The Ohio State University, Columbus, OH 43210, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 1 December 2016 / Revised: 7 February 2017 / Accepted: 12 February 2017 / Published: 16 February 2017
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [462 KB, uploaded 16 February 2017]   |  

Abstract

This paper explores the idea of information loss through data compression, as occurs in the course of any data analysis, illustrated via detailed consideration of the Binomial distribution. We examine situations where the full sequence of binomial outcomes is retained, situations where only the total number of successes is retained, and in-between situations. We show that a familiar decomposition of the Shannon entropy H can be rewritten as a decomposition into H t o t a l , H l o s t , and H c o m p , or the total, lost and compressed (remaining) components, respectively. We relate this new decomposition to Landauer’s principle, and we discuss some implications for the “information-dynamic” theory being developed in connection with our broader program to develop a measure of statistical evidence on a properly calibrated scale. View Full-Text
Keywords: binomial probability distribution; combinatoric coefficient; Shannon entropy; information; data compression; logical irreversibility binomial probability distribution; combinatoric coefficient; Shannon entropy; information; data compression; logical irreversibility
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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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Hodge, S.E.; Vieland, V.J. Information Loss in Binomial Data Due to Data Compression. Entropy 2017, 19, 75.

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