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Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory...
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Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications, 2nd Edition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 2465

Special Issue Editors

Prof. Dr. Brian Dennis

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Guest Editor
1. Department of Mathematics and Statistical Science, University of Idaho, Moscow, ID 83844, USA
2. Department of Fish and Wildlife Sciences, University of Idaho, Moscow, ID 83844, USA
Interests: statistical ecology; biometrics; mathematical modeling; theoretical ecology; conservation biology; population dynamics
Special Issues, Collections and Topics in MDPI journals
Dr. Mark L. Taper

E-Mail Website
Guest Editor
1. Department of Ecology, Montana State University, Bozeman, MT 59717, USA
2. Marine Science Institute, University of California, Santa Barbara, CA 94720, USA
Interests: theoretical ecology; ecological statistics; statistical inference; evolution; philosophy of science
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jose Miguel Ponciano

E-Mail Website
Guest Editor
1. Biology Department , University of Florida, Gainesville, FL 32611, USA
2. Mathematics Department, University of Florida, Gainesville, FL 32611, USA
Interests: statistical ecology; population dynamics; theoretical ecology; statistical phylogenetics; conservation biology; mathematical population genetics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Modern statistical evidence compares the relative support in scientific data for mathematical models. The fundamental tool of comparison is the evidence function, which is a contrast of generalized entropy discrepancies. The most commonly used evidence functions are the differences of information criterion values. Statistical evidence has many desirable properties, combining attractive features of both Bayesian and classical frequentist analysis while simultaneously avoiding many of their philosophical and practical issues. The goals of this Special Issue are to stimulate the further theoretical development of statistical evidence and present real-world examples where the use of statistical evidence clarifies scientific inference. While many of the applications featured here are ecological, reflecting the editors’ areas of expertise, we welcome and anticipate accounts or critiques of evidence functions applied in other scientific areas.

Prof. Dr. Brian Dennis
Dr. Mark L. Taper
Prof. Dr. Jose Miguel Ponciano
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entropy
  • evidential statistics
  • evidence
  • hypothesis testing
  • information theory
  • Kullback–Leibler discrepancy
  • model misspecification
  • model selection

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Related Special Issue

Published Papers (4 papers)

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Research

20 pages, 309 KB  
Article
A Comparison of Algorithms to Achieve the Maximum Entropy in the Theory of Evidence
by Joaquín Abellán, Aina López-Gay, Maria Isabel A. Benítez and Francisco Javier G. Castellano
Entropy 2026, 28(2), 247; https://doi.org/10.3390/e28020247 - 21 Feb 2026
Viewed by 345
Abstract
Within the framework of evidence theory, maximum entropy is regarded as a measure of total uncertainty that satisfies a comprehensive set of mathematical properties and behavioral requirements. However, its practical applicability is severely questioned due to the high computational complexity of its calculation, [...] Read more.
Within the framework of evidence theory, maximum entropy is regarded as a measure of total uncertainty that satisfies a comprehensive set of mathematical properties and behavioral requirements. However, its practical applicability is severely questioned due to the high computational complexity of its calculation, which involves the manipulation of the power set of the frame of discernment. In the literature, attempts have been made to reduce this complexity by restricting the computation to singleton elements, leading to a formulation based on reachable probability intervals. Although this approach relies on a less specific representation of evidential information, it has been shown to provide an equivalent maximum entropy value under certain conditions. In this paper, we present an experimental comparative study of two algorithms for calculating maximum entropy in evidence theory: the classical algorithm, which operates directly on belief functions, and an alternative algorithm based on reachable probability intervals. Through numerical experiments, we demonstrate that the differences between these approaches are less pronounced than previously suggested in the literature. Depending on the type of information representations to which it is applied, the original algorithm based on belief functions can be more efficient than the one using the reachable probability interval approach. This is an interesting result, and a reason for choosing one algorithm over the other depending on the situation. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications, 2nd Edition)
19 pages, 521 KB  
Article
Comparative Evidence-Based Model Choice: A Sketch of a Theory
by Prasanta S. Bandyopadhyay, Samidha Shetty and Gordon Brittan, Jr.
Entropy 2026, 28(1), 13; https://doi.org/10.3390/e28010013 - 23 Dec 2025
Viewed by 530
Abstract
An extensive literature on decision theory has been developed by both subjective Bayesians and Neyman–Pearson (NP) theorists, with more recent contributions to it from evidential decision theorists. The last-mentioned, however, have often been framed from a Bayesian perspective and therefore retain a subjectivist [...] Read more.
An extensive literature on decision theory has been developed by both subjective Bayesians and Neyman–Pearson (NP) theorists, with more recent contributions to it from evidential decision theorists. The last-mentioned, however, have often been framed from a Bayesian perspective and therefore retain a subjectivist orientation. By contrast, we advance a comparative evidence-based model choice (CEMC) account of epistemic utility, which is explicitly non-subjective. On this account, competing models are assessed by the degree to which they are supported by the data and relevant background information, and evaluated comparatively in terms of their relative distances. CEMC thus provides a philosophical framework for inference that integrates the complementary epistemic goals of prediction and explanation. Our approach proceeds in two stages. First, we articulate a framework for non-subjective, non-NP-style, comparative, evidence-based model choice grounded in epistemic utility. Second, we identify statistical tools appropriate for measuring epistemic utility within this framework. We then contrast CEMC with non-comparative evidential decision-theoretic approaches, such as interval-based probability, pioneered by Henry Kyburg, which do not necessarily share the dual aims of explanation and prediction. We conclude by considering the interrelations between prediction, explanation, and model selection criteria, and by showing how these are closely connected with the central commitments of CEMC. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications, 2nd Edition)
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22 pages, 1405 KB  
Article
Entropy-Based Evidence Functions for Testing Dilation Order via Cumulative Entropies
by Mashael A. Alshehri
Entropy 2025, 27(12), 1235; https://doi.org/10.3390/e27121235 - 5 Dec 2025
Viewed by 380
Abstract
This paper introduces novel non-parametric entropy-based evidence functions and associated test statistics for assessing the dilation order of probability distributions constructed from cumulative residual entropy and cumulative entropy. The proposed evidence functions are explicitly tuned to questions about distributional variability and stochastic ordering, [...] Read more.
This paper introduces novel non-parametric entropy-based evidence functions and associated test statistics for assessing the dilation order of probability distributions constructed from cumulative residual entropy and cumulative entropy. The proposed evidence functions are explicitly tuned to questions about distributional variability and stochastic ordering, rather than global model fit, and are developed within a rigorous evidential framework. Their asymptotic distributions are established, providing a solid foundation for large-sample inference. Beyond their theoretical appeal, these procedures act as effective entropy-driven tools for quantifying statistical evidence, offering a compelling non-parametric alternative to traditional approaches, such as Kullback–Leibler discrepancies. Comprehensive Monte Carlo simulations highlight their robustness and consistently high power across a wide range of distributional scenarios, including heavy-tailed models, where conventional methods often perform poorly. A real-data example further illustrates their practical utility, showing how cumulative entropies can provide sharper statistical evidence and clarify stochastic comparisons in applied settings. Altogether, these results advance the theoretical foundation of evidential statistics and open avenues for applying cumulative entropies to broader classes of stochastic inference problems. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications, 2nd Edition)
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23 pages, 1016 KB  
Article
Tsallis Entropy in Consecutive k-out-of-n Good Systems: Bounds, Characterization, and Testing for Exponentiality
by Anfal A. Alqefari, Ghadah Alomani and Mohamed Kayid
Entropy 2025, 27(9), 982; https://doi.org/10.3390/e27090982 - 20 Sep 2025
Viewed by 705
Abstract
This study explores the application of Tsallis entropy in evaluating uncertainty within the framework of consecutive k-out-of-n good systems, which are widely utilized in various reliability and engineering contexts. We derive new analytical expressions and meaningful bounds for the Tsallis entropy [...] Read more.
This study explores the application of Tsallis entropy in evaluating uncertainty within the framework of consecutive k-out-of-n good systems, which are widely utilized in various reliability and engineering contexts. We derive new analytical expressions and meaningful bounds for the Tsallis entropy under various lifetime distributions, offering fresh insight into the structural behavior of system-level uncertainty. The approach establishes theoretical connections with classical entropy measures, such as Shannon and Rényi entropies, and provides a foundation for comparing systems under different stochastic orders. A nonparametric estimator is proposed to estimate the Tsallis entropy in this setting, and its performance is evaluated through Monte Carlo simulations. In addition, we develop a new entropy-based test for exponentiality, building on the distinctive properties of system lifetimes. So, Tsallis entropy serves as a flexible tool in both reliability characterization and statistical inference. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications, 2nd Edition)
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