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]
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Noun1.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 cause
theorem - an idea accepted as a demonstrable truth
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
References in periodicals archive ?
Bayes's theorem provides a method of explicitly including prior events or knowledge when considering the probabilities of current events (for example, including a history of smoking when calculating the probability of developing lung cancer).
6) involves algorithms that learn to assess the probability of statements of the form effect [right arrow] cause by learning the probability of statements of the form cause [right arrow] effect by means of data mining, followed by an application of Bayes's theorem and/or developing a Markov chain.
When total and conditional probabilities in our sample were obtained, it was possible to make probabilistic inferences through Bayes's theorem with the same software.
What mathematicians today call Bayes's theorem is a numerical expression of words by Laplace.
In this context, Grunbaum first argues against what he considers the prima facie most persuasive of the traditional "first cause" cosmological arguments for the existence of God as creator of the universe ex nihilo', second, against theistic explanations of cosmic nomology; third, against the compatibility of divine creation with physical energy conservation in Big Bang cosmology and the physics of steady-state theories; and finally, against Swinburne's attempt to show, via Bayes's theorem, that the existence of God is more probable than not.
In the third section, Silver introduces Bayes's theorem and its applicability to sports and games.
PROVING HISTORY: BAYES'S THEOREM AND THE QUEST FOR THE HISTORICAL JESUS provides a fine discussion of New Testament scholarship and historical challenge, and comes from a historian who proposes Bayes's theorm as a solution to establishing reliable historical criteria over theological controversy.
They discuss the scientific method and the use of Bayes's theorem and describe the proper role of the clinical trial.