Bayes’ theorem

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Bayes’ theorem

Simplistically, Bayes’ theorem is a formula which allows one to find the probability that an event occurred as the result of a particular previous event. It is often used in medicine to determine the mathematical relationship between the probability that an individual has a disease, X, before the test is run, to the probability that the individual has the disease after the test result is known.
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References in periodicals archive ?
He covers characteristics of inverse problems; regularization by spectral filtering; two-dimensional test cases; Bayes' law, Markov random field priors, and maximum a posteriori estimation; and Markov chain Monte Carlo methods for linear and nonlinear inverse problems.
Hansen and Sargent (2007) address these in the context of a model with a representative consumer who responds to assertion 1 by leaving both the i.i.d, and long-run risk models for log consumption growth on the table, attaching a prior initialized at the equal ignorance value of 0.5 to the long-run risk model, then updating by Bayes' law. We show that a consumer who distrusts both submodels and the posterior over submodels that emerges from Bayes' law will behave in a way that supports much of what Bansal and his coauthors do.
Once a user sets values for some nodes, an efficient algorithm that computes Bayes' Law can provide the distribution over the values of any other node.
The private sector updates the probability that the government is NI by use of Bayes' law