A Bayesian update or belief revision is a change in probabilistic beliefs after gaining new knowledge. For example, after observing a patient's test result, we might revise our probability that a patient has a certain disease. If this belief revision obeys Bayes's Rule, then it is called Bayesian.

Bayesian belief updates have a number of other interesting properties, and exemplify many key principles of clear reasoning or rationality. Mapping Bayes's Rule onto real-life problems of encountering new evidence allows us to reproduce many intuitive features that have been suggested for "how to revise beliefs in the face of new evidence".

(Extra)ordinary claims require (extra)ordinary evidence.

The scientific virtues of falsifiability, advance prediction, boldness, precision, and falsificationism can be seen in a Bayesian light.