# Bayesian Probability ## The Idea in Brief Start with what you believe. Update proportionally to the evidence. Don't overreact to noise or underreact to signal. Bayesian thinking is the discipline of calibrated belief revision—treating probability not as a property of the world, but as a measure of your own uncertainty. --- ## Key Concepts ### The Core Mechanic You have a prior—what you believed before seeing new evidence. Evidence arrives. You update your belief proportionally to how surprising that evidence would be under each hypothesis. The result is your posterior—your new belief, ready to become the prior for the next round. The formula (P(H|E) = P(E|H) × P(H) / P(E)) is less important than the intuition: strong evidence updates beliefs a lot; weak evidence updates them a little; evidence that fits equally with both hypotheses updates them not at all. ### Priors Aren't Cheating Frequentists object that priors are "subjective." But you can't escape prior beliefs—everyone has them, explicitly or not. The Bayesian move is to make them visible. State your prior. Show your work. Let others challenge it. The best forecasters have strong priors and update aggressively when evidence contradicts them. The worst have weak priors and update too slowly, or strong priors and refuse to update at all. ### Proportional Updating The discipline is in the "proportionally." A single data point shouldn't swing you from confident to terrified. Nor should you dismiss evidence that contradicts your model. Each piece of evidence gets weighted by its diagnosticity—how much more likely it is under one hypothesis than another. This is where most intuitive reasoning fails. We either lurch in response to vivid anecdotes or dismiss inconvenient data entirely. --- ## Implications **In forecasting:** Superforecasters are essentially Bayesian. They start with base rates, update incrementally, and never treat any belief as too sacred to revise. **In decision-making:** When you're uncertain, explicitly state your probability estimates. When new information arrives, ask: how much should this move me? Usually less than your gut says. **In organisations:** Build systems that score evidence proportionally. Don't let single failures or successes swing strategy. Weight cumulative evidence, not the latest anecdote. --- ## Sources - [[Everything Is Predictable]] — The case for Bayes as the universal framework for reasoning under uncertainty - [[Superforecasting]] — Tetlock's forecasters embody Bayesian updating; they revise constantly, proportionally, and without ego - [[Thinking, Fast and Slow]] — Kahneman on why base rate neglect makes intuitive updating so unreliable --- ## See in Notes - [Decision Architecture](https://www.anishpatel.co/decision-architecture/) — Bayesian updating applied to organisations: score evidence proportionally, don't lurch in response to noise - [Hidden Priors](https://www.anishpatel.co/hidden-priors/) — Why hidden assumptions do most of the work in forecasts