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Entropy 2015, 17(6), 3963-3988; doi:10.3390/e17063963

Most Likely Maximum Entropy for Population Analysis with Region-Censored Data

CNRS, Laboratoire I3S-UMR 7271, Université de Nice-Sophia Antipolis/CNRS, 06900 Sophia Antipolis, France
This paper is an extended version of our paper published in Proceedings of the 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Amboise, France, 21–26 September 2014.
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Author to whom correspondence should be addressed.
Academic Editors: Frédéric Barbaresco and Ali Mohammad-Djafari
Received: 31 January 2015 / Revised: 13 May 2015 / Accepted: 4 June 2015 / Published: 11 June 2015
(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)

Abstract

The paper proposes a new non-parametric density estimator from region-censored observations with application in the context of population studies, where standard maximum likelihood is affected by over-fitting and non-uniqueness problems. It is a maximum entropy estimator that satisfies a set of constraints imposing a close fit to the empirical distributions associated with the set of censoring regions. The degree of relaxation of the data-fit constraints is chosen, such that the likelihood of the inferred model is maximal. In this manner, the estimator is able to overcome the singularity of the non-parametric maximum likelihood estimator and, at the same time, maintains a good fit to the observations. The behavior of the estimator is studied in a simulation, demonstrating its superior performance with respect to the non-parametric maximum likelihood and the importance of carefully choosing the degree of relaxation of the data-fit constraints. In particular, the predictive performance of the resulting estimator is better, which is important when the population analysis is done in the context of risk assessment. We also apply the estimator to real data in the context of the prevention of hyperbaric decompression sickness, where the available observations are formally equivalent to region-censored versions of the variables of interest, confirming that it is a superior alternative to non-parametric maximum likelihood in realistic situations. View Full-Text
Keywords: censored observations; non-parametric maximum likelihood; constrained MaxEnt; regularization censored observations; non-parametric maximum likelihood; constrained MaxEnt; regularization
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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MDPI and ACS Style

Bennani, Y.; Pronzato, L.; Rendas, M.J. Most Likely Maximum Entropy for Population Analysis with Region-Censored Data. Entropy 2015, 17, 3963-3988.

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