Glossary
Bayesian updating
What is Bayesian updating?
Bayesian updating is the process of revising probabilities with new evidence, using Bayes’ theorem. A posterior probability combines a prior probability with the likelihood of the evidence under each hypothesis. The result is normalized across the alternatives considered.
How Bayesian updating works
Griffiths, Kemp, and Tenenbaum’s discussion of Bayesian cognition explains this as a framework for inference under uncertainty. The diagnostic value of evidence depends on how well competing hypotheses predict it, not simply on how surprising it feels.
Worked example
Suppose a hypothetical condition has prior probability 10%, a test is positive in 90% of cases with the condition, and it is positive in 5% of cases without it. A positive result gives 0.90 × 0.10 / (0.90 × 0.10 + 0.05 × 0.90), or about 66.7%. These are illustrative inputs, not facts about a particular medical test.
Why it matters
Bayesian updating gives you an explicit way to combine a starting estimate with new information. A positive test result is more informative when the test rarely gives positives without the condition. Change the prior or the test’s accuracy, and the answer changes.
Researchers also use Bayesian models to study cognition. A model can describe patterns of inference without implying that people consciously calculate Bayes’ theorem.