A probability principle set forth by the English mathematician
Thomas Bayes (1702-1761). Bayes' theorem is of value in medical decision-making
and some of the biomedical sciences.
Bayes' theorem is employed in clinical epidemiology to determine the probability
of a particular disease in a group of people with a specific characteristic on the
basis of the overall rate of that disease and of the likelihood of that specific
characteristic in healthy and diseased individuals, respectively.
A common application of Bayes' theorem is in clinical decision making where it
is used to estimate the probability of a particular diagnosis given the appearance
of specific signs, symptoms, or test outcomes. For example, the accuracy of the
exercise cardiac stress test in predicting significant coronary artery disease (CAD)
depends in part on the "pre-test likelihood" of CAD: the "prior probability" in
Bayes' theorem.
In technical terms, in Bayes' theorem the impact of new data on the merit of
competing scientific hypotheses is compared by computing for each hypothesis the
product of the antecedent plausibility and the likelihood of the current data given
that particular hypothesis and rescaling them so that their total is unity. In Bayes'
theorem:
The antecedent plausibility is termed the "prior probability."
The likelihood of the current data given that particular hypothesis is called
the "conditional probability."
The rescaled values are called the "posterior probabilities."
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