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 (Bayes is the operational engine), critical-thinking (formalizes considering alternatives), logical-fallacies (prosecutor's fallacy and base-rate neglect), and first-principles (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
• A benchmark score, AI-capability claim, AI-adoption stat, or AI-capex/valuation figure is being treated as proof without asking how often that signal appears when the underlying claim is false
• Someone says "Bayesian," "prior," "posterior," "base rate," "likelihood ratio," "update"