Bayes's Theorem

2005 ◽  
Keyword(s):  
Royal Society ◽  
Bayes Theorem ◽  
Criminal Trials ◽  
Probability Calculus ◽  
Strength Of Evidence ◽  
Bayes’S Theorem ◽  
Statistical Science ◽  
Elliott Sober ◽  
Bayes's Theorem

Bayes' theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this book consider the worth and applicability of the theorem. The book sets out the philosophical issues: Elliott Sober argues that there are other criteria for assessing hypotheses; Colin Howson, Philip Dawid, and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles; and David Miller argues for the worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The book ends with the original paper containing the theorem, presented to the Royal Society in 1763.

Glossary of terms

2010 ◽  
pp. 500-506
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Bayesian Statistics ◽  
Analysis Of Variance ◽  
Prior Information ◽  
Statistical Approach ◽  
Bayes Theorem ◽  
Conditional Probabilities ◽  
Unknown Parameters ◽  
Bayes’S Theorem ◽  
Bayes's Theorem

Analysis of variance See One-way analysis of variance (p. 280) and Two-way analysis of variance (p. 412) Bayes’s theorem A formula that allows the reversal of conditional probabilities (see Bayes’ theorem, p. 234) Bayesian statistics A statistical approach based on Bayes’ theorem, where prior information or beliefs are combined with new data to provide estimates of unknown parameters (see ...

A Further Look at Robustness Via Bayes's Theorem

Biometrika ◽  
1962 ◽  
Vol 49 (3/4) ◽  
pp. 419 ◽  
Author(s):  
G. E. P. Box ◽  
G. C. Tiao
Keyword(s):  
Bayes’S Theorem ◽  
Bayes's Theorem

The Weight of Evidence

2021 ◽  
pp. 249-264
Author(s):  
Andrew C. A. Elliott
Keyword(s):  
Weight Of Evidence ◽  
Ecological Fallacy ◽  
Bayes’S Theorem ◽  
Standards Of Proof ◽  
Legal Contexts ◽  
Large Groups ◽  
Bayes's Theorem

Courts of law must weigh evidence to determine the likelihood of competing interpretations of past events, and different legal contexts require different standards of proof, but this falls short of a quantification of probability. Bayes’s theorem and the associated formula provide a way of combining multiple elements of evidence and using them to refine prior assessments of probability. The prosecutor’s fallacy involves an incorrect reversal of the logic of evidence. The ecological fallacy involves incorrectly attributing proportions derived from large groups to smaller groups or individuals.

Bayes’s Theorem

2021 ◽  
pp. 1-4
Author(s):  
Konstantinos Modis
Keyword(s):  
Bayes’S Theorem ◽  
Bayes's Theorem

Application of Bayes's theorem to results of quantitative clinical chemical determinations.

1979 ◽  
Vol 25 (6) ◽  
pp. 985-988 ◽  
Author(s):  
H J van der Helm ◽  
E A Hische
Keyword(s):  
Likelihood Ratio ◽  
Predictive Values ◽  
Logical Approach ◽  
Convenient Form ◽  
Bayes’S Theorem ◽  
Clinical Chemical ◽  
Laboratory Results ◽  
Single Number ◽  
Bayes's Theorem ◽  
Test Result

Abstract The diagnostic implication of a certain test result with regard to a certain condition can be expressed as a single number, L, the likelihood ratio of this result. This ratio allows Bayes's theorem to be written in a convenient form. We show that the practice of calculating predictive values for the results of quantitative tests by use of discrimination limits leads to incorrect predictive values. Including L values in laboratory reports seems a more logical approach to optimum interpretation of laboratory results than the use of discrimination values.

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