Bayesian Inference
Source: Thomas Bayes, 1763 (posthumous); Pierre-Simon Laplace, 1774
Finding
Bayes’ theorem: P(H|E) = P(E|H) * P(H) / P(E). The posterior probability of a hypothesis given evidence is proportional to the likelihood of evidence given hypothesis, times the prior. It is the mathematically correct way to update beliefs in light of new evidence. A strong prior should yield to strong contrary evidence. Without evidence, the posterior equals the prior. The framework prevents generating confidence where none is warranted.
Pattern Mapping
Honesty — Bayesian inference formalizes what honesty demands: beliefs should change in proportion to evidence. Refusing to update — holding a prior fixed regardless of data — is the mathematical equivalent of dishonesty.
Proportion — The update is exactly proportional to evidence strength. Weak evidence produces small updates; strong evidence produces large ones. No overcorrection (fabricated certainty) or undercorrection (fabricated doubt).
Humility — The prior acknowledges what you believed before evidence arrived. Making the prior explicit is an act of humility: admitting your starting position rather than pretending to begin from nowhere.
Non-fabrication — Bayesian inference does not allow manufacturing certainty from nothing. Without discriminating evidence, the posterior equals the prior.
Connections
- Testing — both update confidence based on evidence (→ Meta-Pattern 01)
- Error-Correcting Codes — both are formal frameworks for maintaining signal integrity
- Photoelectric Effect — Millikan’s honest updating despite theoretical commitments
- Technical Debt — failing to update code is refusing to update beliefs
- Propaganda — propaganda exploits those who fail to update: the Big Lie persists despite evidence
Status
Established probability theory. See Jaynes, Probability Theory: The Logic of Science (2003); Gelman et al., Bayesian Data Analysis (3rd ed., 2013). The mapping is this project’s interpretation, though “rational belief revision” is standard epistemology.
The mapping to the five properties is this project’s structural interpretation.