# Bayes' theorem Evidence doesn't give you the answer. It moves the answer from wherever it was before you looked. Skip the starting point and the evidence misleads you. --- ## The mechanics A prior: what you believed before seeing new evidence. A likelihood: how probable the evidence is if your hypothesis is true. A posterior: your updated belief after seeing the evidence. **P(H|E) = P(E|H) × P(H) / P(E)** The formula is straightforward. What it enforces is harder: before interpreting any evidence, state what you believed beforehand and why. Then ask how strongly the evidence discriminates between your hypothesis and the alternatives. The posterior combines both. --- ## The prior shapes the answer A 95% accurate test sounds decisive, but if the condition affects one person in a thousand, a positive result is still overwhelmingly likely to be a false alarm. The accuracy of the test matters less than the prevalence of the condition. [[Bases]] walks through this in a hiring context. A recruiter with 90% screening accuracy delivers a coin flip when only one in ten candidates in the pool is genuinely good. Improving the pool to one in three does more than improving the test to 99%. [[Priors]] applies the same structure to churn prediction. A customer goes to tender and the historical churn rate for tendering customers is 75%. But this account was at 5% risk yesterday. Bayes moves the number to 25%, not 75%. The evidence shifted the prior; it didn't replace it. --- ## The updating discipline Without a stated prior, new information becomes confirmation bias with better vocabulary. A positive result confirms your thesis. A negative one was underpowered. Both feel reasonable because neither is anchored to what you believed before looking. [[Everything Is Predictable]] makes the case that refusing to state priors doesn't make you objective. It makes inference impossible. The priors don't disappear; they hide inside methodological choices: which tests to run, when to stop collecting data, how to define significance. Making them explicit forces the discipline of justifying them and showing how evidence changes them. [[Superforecasting]] confirms empirically that the forecasters who beat the odds anchor to base rates first, adjust for specifics, then track and update. The method is Bayesian whether or not they use the word. [[Unknown and unknowable]] sits at the boundary where Bayes runs out. Some signals never arrive in a form you can process: the competitor cultivating your customer's CFO over dinner, the board-level merger you'll never hear about. Bayes is the right framework for what you can observe. Recognising where observation ends is the adjacent skill.