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 ...

Evidence and Probability Data

2019 ◽  
pp. 83-100
Author(s):  
Steven J. Osterlind
Keyword(s):  
United States ◽  
Bayesian Estimation ◽  
Cancer Diagnosis ◽  
The United States ◽  
Protestant Ethic ◽  
Conditional Probabilities ◽  
Billiard Table ◽  
Bayes’S Theorem ◽  
Magnum Opus ◽  
Bayes's Theorem

This chapter discusses evidence and probability data with particular attention on Bayesian estimation. The Protestant ethic slowed probability developments in the United States, but the idea of quantification continued apace in England and on the Continent. In particular, Thomas Bayes invented a simple but profound mathematical means to connect outcomes with causes with conditional probabilities and Bayesian estimation. The chapter explains conditional probabilities and Bayesian logic, giving several examples, including incidence of accurate cancer diagnosis with inexact diagnostics. The chapter also introduces Bayes’s magnum opus An Essay Toward Solving a Problem in the Doctrine of Chances and gives his example of rolling billiard balls on a billiard table to show Bayes’s theorem.

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.

scholarly journals Characterization of the Bayesian Posterior Distribution in Terms of Self-information

2017 ◽  
Vol 7 (1) ◽  
pp. 21
Author(s):  
Marco Dall'Aglio ◽  
Theodore P. Hill
Keyword(s):  
Bayesian Statistics ◽  
Unique Solution ◽  
Posterior Distribution ◽  
Optimization Problems ◽  
Probability Distributions ◽  
Bayes Theorem ◽  
Conditional Probabilities ◽  
Loss Of Self

It is well known that the classical Bayesian posterior arises naturally as the unique solution of different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. Here it is shown that the Bayesian posterior is also the unique minimax optimizer of the loss of self-information in combining the prior and the likelihood distributions, and is the unique proportional consolidation of the same distributions. These results, direct corollaries of recent results about conflations of probability distributions, further reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.

The Application of Bayesian Statistics in Calculating Project Buffer

2011 ◽  
Vol 58-60 ◽  
pp. 1018-1024
Author(s):  
Feng Ye ◽  
Gui Chen Xu ◽  
Di Kang Zhu
Keyword(s):  
Bayesian Statistics ◽  
Statistical Approach ◽  
Implementation Process ◽  
Current Method ◽  
Practical Application ◽  
Great Flexibility ◽  
Crystal Ball ◽  
Simulation Results ◽  
The Stability

This paper reviews several current methods of calculating buffer on the basis of pointing out each merits and pitfalls and then introduces Bayesian statistical approach to CCS / BM domain to calculate the size of the project buffer, to overcome that the current method of the buffer calculation is too subjective and the defect on lacking of practical application. In Crystal Ball, we compare the simulation results of implementation process on the benchmark of C&PM, RESM and SM. The results show that the buffer using this method can ensure the stability of the project’s completion probability, and this method has great flexibility.

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
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