bayesian-reasoninglisted

# Bayesian Reasoning ## Overview Bayes' theorem: **Posterior odds = Prior odds × Likelihood ratio**. The strength of belief after evidence equals the strength before, multiplied by how diagnostic the evidence is. This skill applies Bayesian discipline where people reason about probabilities informally — and failures follow predictable patterns: ignoring the base rate (prior), confusing P(E|H) with P(H|E) (prosecutor's fallacy), over-updating on vivid confirming evidence, treating correlated evidence as independent. Composes with [`probabilistic-thinking`](../probabilistic-thinking/SKILL.md) (Bayes is the operational engine), [`critical-thinking`](../critical-thinking/SKILL.md) (formalizes considering alternatives), [`logical-fallacies`](../logical-fallacies/SKILL.md) (prosecutor's fallacy and base-rate neglect), and [`first-principles`](../first-principles/SKILL.md) (the prior is bedrock). ## When to Use - High-stakes decision rests on interpreting evidence (medical test, security alert, fraud flag, hiring signal, A/B result) - "Evidence is consistent with X" is being treated as proof of X - Base rates ignored — a rare event treated as probable because evidence "looks like" it - Correlated evidence pieces treated as independent updates - Someone says "Bayesian," "prior," "posterior," "base rate," "likelihood ratio," "update" **Not when:** genuinely deterministic; no data to anchor a prior; cost of formal update exceeds the value of being more right. ## Coaching Novice