Belief Updating¶
Summary¶
The process of revising probabilities assigned to hypotheses as new evidence becomes available — the core mechanism of Bayesian reasoning.
The Update Cycle¶
Prior belief → New evidence → Likelihood calculation → Posterior belief → New prior
Each posterior becomes the prior for the next round — beliefs evolve iteratively.
How Much Should Beliefs Change?¶
The amount of change depends on two factors: 1. Strength of prior — Strong priors require more evidence to shift 2. Diagnosticity of evidence — Evidence that's much more likely under one hypothesis than another causes bigger shifts
Principles¶
- Irrelevant evidence doesn't change beliefs — If P(E|H) = P(E|¬H), posterior = prior
- Strong priors resist weak evidence — Extraordinary claims require extraordinary evidence
- Multiple weak evidence can combine — Each piece shifts the posterior incrementally