The Reverend Thomas Bayes was an 18th-century Presbyterian minister and mathematician. An important theorem he developed late in his life is now known as Bayes theorem.

Bayesian probability theory specifies how we should update our belief in the likelihood of something given new evidence or data. Bayesian probability is not intuitive and is not well understood by many people, including some doctors.

Consider the case of medical diagnostic testing. We start with a patient who we are concerned might have a particular disease. Our estimate of how likely it is that they have the disease is the ‘prior probability’.

Once we carry out the diagnostic test, we can use Bayes theorem to work out how to use the results of the testing to update the probability that the patient has the disease. This revised estimate is the ‘posterior’ or ‘post-test probability’.