# theorem

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Related to Bayes' theorem: conditional probability
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Bayes' theorem tells us that the value of a piece of evidence in testing a particular assertion is determined by its likelihood ratio.
Applying Bayes | Police detectives generally understand the concepts behind Bayes' Theorem, even if they do not know the mathematical or quantitative formulation.
Bayes' theorem combines all the elements required to derive a probability that a hypothesis is true, including considerations of study power.
Bayes' Theorem can also be written as Equation 3 below where ([alpha]) consists of the set of (m) parameters of the cumulative (unknown) distribution [PHI]( x | [alpha] ).
Bayes' theorem is described in terms of conditional probabilities, and the likelihood ratio approach is ignored, although he had previously introduced the concept of odds.
Now remember the simple formulation of Bayes' Theorem, that the posterior odds equal the prior odds times the likelihood ratio.
Bayes' Theorem states: The joint probability of two correlated occurrences A and C equals the conditional probability of A if C times the prior probability of C or inversely the conditional probability of C if A times the prior probability of A.
The late-lamented, and much missed, Alvin Feinstein (who trained as a mathematician before qualifying in medicine) described the use of probabilities and conditional probabilities to express Bayes' theorem as "one of medical literature's greatest communicative terrors .
For instance, psychologists have for 35 years repeatedly assessed whether people make inferences according to Bayes' theorem, a mathematical formula that can be used to estimate an individual's expectation that a particular event will occur.

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