Definition of Bayes theorem

Bayes theorem: 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."