Coherently updating degrees of belief: Radical Probabilism, the generalization of Bayes’ Theorem and its consequences on evidence evaluation

IF 1.4 4区社会学 Q1 LAW

Law Probability & Risk Pub Date : 2020-12-01 DOI:10.1093/LPR/MGAB001

F. Taroni, Paolo Garbolino, S. Bozza

引用次数: 1

Abstract

The Bayesian perspective is based on conditioning related to reported evidence that is considered to be certain. What is called ‘Radical Probabilism’ replaces such an extreme view by introducing uncertainty on the reported evidence. How can such equivocal evidence be used in further inferences about a main hypothesis? The theoretical ground is introduced with the aim of offering to the readership an explanation for the generalization of the Bayes’ Theorem. This extension—that considers uncertainty related to the reporting of evidence—also has an impact on the assessment of the value of evidence through the Bayes’ factor. A generalization for such a logical measure of the evidence is also presented and justified.

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连贯更新信念度:激进概率、贝叶斯定理的推广及其对证据评价的影响

贝叶斯观点是基于与被认为是确定的报告证据相关的条件作用。所谓的“激进概率论”通过在报告的证据上引入不确定性来取代这种极端观点。这种模棱两可的证据如何用于对主要假设的进一步推断?介绍贝叶斯定理的理论基础，目的是为读者提供一个概括贝叶斯定理的解释。这种扩展-考虑到与证据报告相关的不确定性-也通过贝叶斯因子对证据价值的评估产生影响。还提出并证明了对这种证据的逻辑度量的概括。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Law Probability & Risk MATHEMATICSSTATISTICS & PROBABILITY&-STATISTICS & PROBABILITY

CiteScore

2.10

自引率

28.60%

发文量

期刊介绍： Law, Probability & Risk is a fully refereed journal which publishes papers dealing with topics on the interface of law and probabilistic reasoning. These are interpreted broadly to include aspects relevant to the interpretation of scientific evidence, the assessment of uncertainty and the assessment of risk. The readership includes academic lawyers, mathematicians, statisticians and social scientists with interests in quantitative reasoning. The primary objective of the journal is to cover issues in law, which have a scientific element, with an emphasis on statistical and probabilistic issues and the assessment of risk. Examples of topics which may be covered include communications law, computers and the law, environmental law, law and medicine, regulatory law for science and technology, identification problems (such as DNA but including other materials), sampling issues (drugs, computer pornography, fraud), offender profiling, credit scoring, risk assessment, the role of statistics and probability in drafting legislation, the assessment of competing theories of evidence (possibly with a view to forming an optimal combination of them). In addition, a whole new area is emerging in the application of computers to medicine and other safety-critical areas. New legislation is required to define the responsibility of computer experts who develop software for tackling these safety-critical problems.