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Entropy
Volume 27
Issue 8
10.3390/e27080865
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Article

Variations on the Expectation Due to Changes in the Probability Measure

by
Samir M. Perlaza
1,2,3,* and
Gaetan Bisson
3
1
Centre Inria d’Université Côte d’Azur, INRIA, Sophia Antipolis, 06902, France
2
Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA
3
GAATI Mathematics Laboratory, University of French Polynesia, 98702 Faaa, French Polynesia
*
Author to whom correspondence should be addressed.
Entropy 2025, 27(8), 865; https://doi.org/10.3390/e27080865
Submission received: 23 July 2025 / Revised: 11 August 2025 / Accepted: 12 August 2025 / Published: 14 August 2025
(This article belongs to the Section Information Theory, Probability and Statistics)
Review Reports Versions Notes

Abstract

In this paper, closed-form expressions for the variation of the expectation of a given function due to changes in the probability measure (probability distribution drifts) are presented. These expressions unveil interesting connections with Gibbs probability measures, information projections, Pythagorean identities for relative entropy, mutual information, and lautum information.
Keywords: Gibbs probability measures; Pythagorean identities; sensitivity; probability distribution drifts; variations of the expectation Gibbs probability measures; Pythagorean identities; sensitivity; probability distribution drifts; variations of the expectation

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MDPI and ACS Style

Perlaza, S.M.; Bisson, G. Variations on the Expectation Due to Changes in the Probability Measure. Entropy 2025, 27, 865. https://doi.org/10.3390/e27080865

AMA Style

Perlaza SM, Bisson G. Variations on the Expectation Due to Changes in the Probability Measure. Entropy. 2025; 27(8):865. https://doi.org/10.3390/e27080865

Chicago/Turabian Style

Perlaza, Samir M., and Gaetan Bisson. 2025. "Variations on the Expectation Due to Changes in the Probability Measure" Entropy 27, no. 8: 865. https://doi.org/10.3390/e27080865

APA Style

Perlaza, S. M., & Bisson, G. (2025). Variations on the Expectation Due to Changes in the Probability Measure. Entropy, 27(8), 865. https://doi.org/10.3390/e27080865

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