Updating Your Beliefs

Bayes' theorem tells you how to revise a probability when new evidence arrives. Before a medical test, your chance of having a rare disease might be 1 in 1,000. A positive result does not mean you definitely have it, because false positives exist. The theorem combines three things: how likely the disease was before the test, the test's accuracy, and its false positive rate.

Thomas Bayes worked this out in the 1700s. Today it powers spam filters, medical diagnostics, and machine learning.