Mind · Inference
BayesUpdate
Mathematically rigorous belief revision
Definition
Mechanism
Likelihood Weighting: Hold prior probability P(H). Observe evidence E. Compute likelihood ratio P(E|H)/P(E|¬H). Convert the prior to odds, multiply by the ratio, convert back to a probability. Large ratio = strong update. Ratio near 1 = weak evidence. Never update to 0 or 1. It explicitly incorporates BaseRateInclude into the prior probability calculation to prevent base-rate neglect.
Preconditions
- Prior probability defined in (0,1)
- New evidence observed.
- Likelihood computable.
Postconditions
- Posterior probability in (0,1)
- Belief updated proportional to evidence strength.
- Prior recoverable from the posterior and the ratio, unless the posterior was clamped.
Invariants
- The posterior odds are the prior odds scaled by the likelihood ratio P(E|H)/P(E|not H).
- Prior and posterior both stay at least `clamp` away from 0 and 1.
Risks
Failure modes
Prior Dogmatism
Setting a prior of 1.0 or 0.0 prevents any future updating, regardless of evidence.
Relationships
Builds on
References
Outside view over inside view
Infrastructure
A subjective claim with confidence and evidence
Infrastructure
Active State Perception
Used by
References
Aligning subjective confidence with objective frequency
Bayesian belief updating via falsification rungs
Reference
Parameters
clampProbability, (0.0, 0.5)- Distance from 0 and 1 that no probability may cross, so evidence can always move it.