Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play
Empirical Bayes-based Methods (<i>EBM</i>) is an increasingly popular form of Objective Bayesianism (<i>OB</i>). It is identified in particular with the statistician Bradley Efron. The main aims of this paper are, first, to describe and illustrate its main features and, secon...
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2024-10-01
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| author | Samidha Shetty Gordon Brittan Prasanta S. Bandyopadhyay |
| author_facet | Samidha Shetty Gordon Brittan Prasanta S. Bandyopadhyay |
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| description | Empirical Bayes-based Methods (<i>EBM</i>) is an increasingly popular form of Objective Bayesianism (<i>OB</i>). It is identified in particular with the statistician Bradley Efron. The main aims of this paper are, first, to describe and illustrate its main features and, second, to locate its role by comparing it with two other statistical paradigms, Subjective Bayesianism (<i>SB</i>) and Evidentialism<i>. EBM</i>’s main formal features are illustrated in some detail by schematic examples. The comparison between what Efron calls their underlying “philosophies” is by way of a distinction made between confirmation and evidence. Although this distinction is sometimes made in the statistical literature, it is relatively rare and never to the same point as here. That is, the distinction is invariably spelled out intra- and not inter-paradigmatically solely in terms of one or the other accounts. The distinction made in this paper between confirmation and evidence is illustrated by two well-known statistical paradoxes: the base-rate fallacy and Popper’s paradox of ideal evidence. The general conclusion reached is that each of the paradigms has a basic role to play and all are required by an adequate account of statistical inference from a technically informed and fine-grained philosophical perspective. |
| format | Article |
| id | doaj-art-00f62fe39f7e401cac5c83655b1efa45 |
| institution | OA Journals |
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| language | English |
| publishDate | 2024-10-01 |
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| spelling | doaj-art-00f62fe39f7e401cac5c83655b1efa452025-08-20T02:11:00ZengMDPI AGEntropy1099-43002024-10-01261085910.3390/e26100859Empirical Bayes Methods, Evidentialism, and the Inferential Roles They PlaySamidha Shetty0Gordon Brittan1Prasanta S. Bandyopadhyay2Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USADepartment of History and Philosophy, Montana State University, Bozeman, MT 59717, USADepartment of History and Philosophy, Montana State University, Bozeman, MT 59717, USAEmpirical Bayes-based Methods (<i>EBM</i>) is an increasingly popular form of Objective Bayesianism (<i>OB</i>). It is identified in particular with the statistician Bradley Efron. The main aims of this paper are, first, to describe and illustrate its main features and, second, to locate its role by comparing it with two other statistical paradigms, Subjective Bayesianism (<i>SB</i>) and Evidentialism<i>. EBM</i>’s main formal features are illustrated in some detail by schematic examples. The comparison between what Efron calls their underlying “philosophies” is by way of a distinction made between confirmation and evidence. Although this distinction is sometimes made in the statistical literature, it is relatively rare and never to the same point as here. That is, the distinction is invariably spelled out intra- and not inter-paradigmatically solely in terms of one or the other accounts. The distinction made in this paper between confirmation and evidence is illustrated by two well-known statistical paradoxes: the base-rate fallacy and Popper’s paradox of ideal evidence. The general conclusion reached is that each of the paradigms has a basic role to play and all are required by an adequate account of statistical inference from a technically informed and fine-grained philosophical perspective.https://www.mdpi.com/1099-4300/26/10/859James-Stein estimatorBeta-Binomial distributionconfirmation/evidence distinctionSubjective BayesianismObjective Bayesianismbase-rate fallacy |
| spellingShingle | Samidha Shetty Gordon Brittan Prasanta S. Bandyopadhyay Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play Entropy James-Stein estimator Beta-Binomial distribution confirmation/evidence distinction Subjective Bayesianism Objective Bayesianism base-rate fallacy |
| title | Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play |
| title_full | Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play |
| title_fullStr | Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play |
| title_full_unstemmed | Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play |
| title_short | Empirical Bayes Methods, Evidentialism, and the Inferential Roles They Play |
| title_sort | empirical bayes methods evidentialism and the inferential roles they play |
| topic | James-Stein estimator Beta-Binomial distribution confirmation/evidence distinction Subjective Bayesianism Objective Bayesianism base-rate fallacy |
| url | https://www.mdpi.com/1099-4300/26/10/859 |
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