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Open AccessArticle

Information Loss in Binomial Data Due to Data Compression

by Susan E. Hodge 1,2 and Veronica J. Vieland 1,2,3,*
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
Entropy 2017, 19(2), 75; https://doi.org/10.3390/e19020075
Received: 1 December 2016 / Revised: 7 February 2017 / Accepted: 12 February 2017 / Published: 16 February 2017
(This article belongs to the Section Information Theory, Probability and Statistics)
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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Hodge, S.E.; Vieland, V.J. Information Loss in Binomial Data Due to Data Compression. Entropy 2017, 19, 75.

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