# Bayes' theorem

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## Bayes' theorem

(beɪz)
n
(Statistics) statistics the fundamental result which expresses the conditional probability P(E/A) of an event E given an event A as P(A/E).P(E)/P(A); more generally, where En is one of a set of values Ei which partition the sample space, P(En/A) = P(A/En)P(En)/Σ P(A/Ei)P(Ei). This enables prior estimates of probability to be continually revised in the light of observations
[C20: named after Thomas Bayes (1702–61), English mathematician and Presbyterian minister]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Bayes' theorem - (statistics) a theorem describing how the conditional probability of a set of possible causes for a given observed event can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each causetheorem - an idea accepted as a demonstrable truthstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
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References in periodicals archive ?
If the main cause is improper Bayesian updating following restricted choice, then the Monty Hall problem is a decisiontheoretic manifestation of longstanding statistical puzzles in education, psychology, and sports science (Miller and Sanjurjo 2015) and in medical decision-making (Cox et al.
propose a fusion algorithm to combine the excellent modeling ability of Bayesian updating method for the multilevel data and the prominent estimation ability of ECM algorithm for incomplete data.
The combination of prior distribution of fatigue crack growth model parameters with experimental observations can be carried out by applying the concepts of Bayesian updating. The results from updated distribution function are also termed as posterior distribution.
Au, "Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation," Journal of Engineering Mechanics, vol.
The chapter ends by concluding (1) if regulatory agencies use PRA without Bayesian updating and (2) if the propensity to invest in nuclear safety is not brought under control, then "many expensive new protective measures will accumulate, without necessarily having any effect." (p.
 stablished the foundations from which the efficacy of Bayesian updating in competing risks problems can be assessed, as the efficacy of Bayes estimators in such contexts (nonidentifiability) has received rather little attention.
The issue that is the focus of Quitting Certainties concerns the inability of the traditional Bayesian updating rule to properly model claims that move from certainty to uncertainty.
One goal of Digital Twin is to identify the effect of such gaps while a vehicle is in-service and provide a means of filling them via Bayesian updating and model improvements.
A recently proposed pathophysiological model of phantom sound based on a predictive brain concept with Bayesian updating  might explain why tinnitus is not perceived during dreaming.
A derivation of field equations for a unit charge with a single spherical Dirichlet boundary condition shows the consistency of this approach with sequential updating principles as used in Bayesian updating.
Beck, "Bayesian updating and model class selection for hysteretic structural models using stochastic simulation," JVC/Journal of Vibration and Control, vol.
The interactions within a neighborhood are performed through a sequential Bayesian updating process .

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