# Bayes' theorem

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Related to Bayesian updating: Bayesian analysis, Bayesian approach

## 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]
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
References in periodicals archive ?
30] 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.
Most studies of Bayesian updating use experimental data.
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.
Among the topics are methods for modeling failure scenarios, uncertainties in geotechnical data, physical and polynomial response surfaces, Bayesian updating techniques in structural reliability, and maintenance cost models.
Assuming Bayesian updating model of stock price distributions, this study shows how underpricing can be used to increase existing owners' wealth through the IPO process.
In this article, we study the implications of this double information-asymmetry insurance problem in a multiperiod model with the insurer learning through Bayesian updating.
Thus, without any Bayesian updating with new data, each captain's inputs are given equal weight in the output probability distribution [q.
This quality can be assured in several ways the first of which is applying local data on sprinkler failures used as new evidence for Bayesian updating.
Their topics include Bayesian updating, representations, computation, data structures, the nature of learning, dead reckoning in a neural network, and the molecular basis of memory.
Another reason why the benefits of experimentation are small is that Bayesian updating makes posterior model probabilities a martingale (Doob, 1948), implying [E.

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