Bayesian update

by Eliezer Yudkowsky Jan 15 2016 updated Feb 8 2017

Bayesian updating: the ideal way to change probabilistic beliefs based on evidence.

[summary: Bayesian updating or Bayesian belief revision is a way of changing probabilistic beliefs, in response to evidence, in a way that obeys Probability theory and in particular Bayes' rule.

When we observe a piece of evidence that is more likely to be seen if X is true than if X is false, we should assign more credence to X. For example, if I take a random object from your kitchen, and then I tell you this object is sharp, you should assign more credence than you did previously that it's a knife (even though forks are also sharp, so you won't be certain).

For more on this subject see the Arbital guide to Bayes's rule.]

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".