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Entropy
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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

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 4722

Special Issue Editors

Prof. Dr. Brian Dennis

E-Mail Website
Guest Editor
1. Department of Mathematics and Statistical Science, University of Idaho, Moscow, ID 83844, USA
2. Professor Emeritus, 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
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
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 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. 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 100 words) can be sent to the Editorial Office for announcement on this website.

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

Published Papers (4 papers)

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Editorial

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8 pages, 251 KiB  
Editorial
Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications
by Mark L. Taper, José Miguel Ponciano and Brian Dennis
Entropy 2022, 24(9), 1273; https://doi.org/10.3390/e24091273 - 09 Sep 2022
Viewed by 1189
Abstract
Scope and Goals of the Special Issue: There is a growing realization that despite being the essential tool of modern data-based scientific discovery and model testing, statistics has major problems [...] Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications)

Research

Jump to: Editorial

23 pages, 501 KiB  
Article
How the Post-Data Severity Converts Testing Results into Evidence for or against Pertinent Inferential Claims
by Aris Spanos
Entropy 2024, 26(1), 95; https://doi.org/10.3390/e26010095 - 22 Jan 2024
Viewed by 669
Abstract
The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It [...] Read more.
The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It is argued that this contributes to the untrustworthiness problem in several different ways, including [a] statistical misspecification, [b] unwarranted evidential interpretations of frequentist inference results, and [c] questionable modeling strategies that rely on curve-fitting. What is more, the alternative proposals to replace or modify frequentist testing, including [i] replacing p-values with observed confidence intervals and effects sizes, and [ii] redefining statistical significance, will not address the untrustworthiness of evidence problem since they are equally vulnerable to [a]–[c]. The paper calls for distinguishing between unduly data-dependant ‘statistical results’, such as a point estimate, a p-value, and accept/reject H0, from ‘evidence for or against inferential claims’. The post-data severity (SEV) evaluation of the accept/reject H0 results, converts them into evidence for or against germane inferential claims. These claims can be used to address/elucidate several foundational issues, including (i) statistical vs. substantive significance, (ii) the large n problem, and (iii) the replicability of evidence. Also, the SEV perspective sheds light on the impertinence of the proposed alternatives [i]–[iii], and oppugns [iii] the alleged arbitrariness of framing H0 and H1 which is often exploited to undermine the credibility of frequentist testing. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications)
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14 pages, 334 KiB  
Article
Profile Likelihood for Hierarchical Models Using Data Doubling
by Subhash R. Lele
Entropy 2023, 25(9), 1262; https://doi.org/10.3390/e25091262 - 25 Aug 2023
Viewed by 708
Abstract
In scientific problems, an appropriate statistical model often involves a large number of canonical parameters. Often times, the quantities of scientific interest are real-valued functions of these canonical parameters. Statistical inference for a specified function of the canonical parameters can be carried out [...] Read more.
In scientific problems, an appropriate statistical model often involves a large number of canonical parameters. Often times, the quantities of scientific interest are real-valued functions of these canonical parameters. Statistical inference for a specified function of the canonical parameters can be carried out via the Bayesian approach by simply using the posterior distribution of the specified function of the parameter of interest. Frequentist inference is usually based on the profile likelihood for the parameter of interest. When the likelihood function is analytical, computing the profile likelihood is simply a constrained optimization problem with many numerical algorithms available. However, for hierarchical models, computing the likelihood function and hence the profile likelihood function is difficult because of the high-dimensional integration involved. We describe a simple computational method to compute profile likelihood for any specified function of the parameters of a general hierarchical model using data doubling. We provide a mathematical proof for the validity of the method under regularity conditions that assure that the distribution of the maximum likelihood estimator of the canonical parameters is non-singular, multivariate, and Gaussian. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications)
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16 pages, 924 KiB  
Article
Evidence of an Absence of Inbreeding Depression in a Wild Population of Weddell Seals (Leptonychotes weddellii)
by John H. Powell, Steven T. Kalinowski, Mark L. Taper, Jay J. Rotella, Corey S. Davis and Robert A. Garrott
Entropy 2023, 25(3), 403; https://doi.org/10.3390/e25030403 - 22 Feb 2023
Viewed by 1410
Abstract
Inbreeding depression can reduce the viability of wild populations. Detecting inbreeding depression in the wild is difficult; developing accurate estimates of inbreeding can be time and labor intensive. In this study, we used a two-step modeling procedure to incorporate uncertainty inherent in estimating [...] Read more.
Inbreeding depression can reduce the viability of wild populations. Detecting inbreeding depression in the wild is difficult; developing accurate estimates of inbreeding can be time and labor intensive. In this study, we used a two-step modeling procedure to incorporate uncertainty inherent in estimating individual inbreeding coefficients from multilocus genotypes into estimates of inbreeding depression in a population of Weddell seals (Leptonychotes weddellii). The two-step modeling procedure presented in this paper provides a method for estimating the magnitude of a known source of error, which is assumed absent in classic regression models, and incorporating this error into inferences about inbreeding depression. The method is essentially an errors-in-variables regression with non-normal errors in both the dependent and independent variables. These models, therefore, allow for a better evaluation of the uncertainty surrounding the biological importance of inbreeding depression in non-pedigreed wild populations. For this study we genotyped 154 adult female seals from the population in Erebus Bay, Antarctica, at 29 microsatellite loci, 12 of which are novel. We used a statistical evidence approach to inference rather than hypothesis testing because the discovery of both low and high levels of inbreeding are of scientific interest. We found evidence for an absence of inbreeding depression in lifetime reproductive success, adult survival, age at maturity, and the reproductive interval of female seals in this population. Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications)
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