Bayes’s Theorem

Bayes’s theorem is a way of estimating the likelihood of some event having occurred, or some condition being true, given some evidence that is related to the event or condition. This entry describes how Bayes’s theorem is used, discusses three forms of the theorem, and provides detailed examples of the use of the theorem.

Throughout the sciences, we are faced with questions about how likely an event of interest is, given some information. For example,

• How likely is a student to achieve at least a certain level of academic performance in the future, given the student’s past performance?
• What is the probability that a patient has a certain disease, given the patient’s diagnostic test results and background health information?
• How likely is it that a defendant is guilty of ...