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”.
The scientific virtues of falsifiability, advance prediction, boldness, precision, and falsificationism can be seen in a Bayesian light.
- Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don’t provide quantitatively enough evidence.
- Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes’ rule, of course.
- Strength of Bayesian evidence
From a Bayesian standpoint, the strength of evidence can be identified with its likelihood ratio.
- Path: Insights from Bayesian updating
A learning-path placeholder page for insights derived from the Bayesian rule for updating beliefs.
- Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims don’t.
- Bayesian reasoning
A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence.