Bayes' Theorem
A mathematical framework for updating beliefs based on new evidence.
Also known as: Bayesian reasoning, Bayesian inference, Belief updating
Category: Concepts
Tags: statistics, probabilities, thinking, decision-making, mathematics
Explanation
Bayes' theorem is a mathematical formula for updating the probability of a hypothesis based on new evidence. It answers: given what I now know, how should I revise my beliefs? The formula: P(H|E) = P(E|H) × P(H) / P(E) - the probability of hypothesis given evidence equals likelihood of evidence given hypothesis, times prior probability, divided by overall evidence probability. In practice: start with a prior belief (base rate), observe evidence, update belief proportionally to how much that evidence supports the hypothesis. Bayesian thinking involves: acknowledging uncertainty in beliefs, updating incrementally with new information, weighing evidence by its diagnosticity, and maintaining calibrated confidence. Key insights: strong priors require strong evidence to change, some evidence is more diagnostic than others, and beliefs should change gradually with evidence. Bayesian reasoning helps avoid: overconfidence (priors often too extreme), underweighting evidence (not updating enough), and base rate neglect (ignoring priors entirely). For knowledge workers, Bayesian thinking provides: a framework for reasoning under uncertainty, a way to integrate new information systematically, and a mindset of probabilistic rather than binary beliefs.
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