principles.fyi · the brain · concept

prior

Where your belief stands before the new evidence arrives — the starting point of the walk.

posterior log-odds = prior log-odds + evidence points

The prior is your probability for something before seeing the evidence at hand: how rare the disease is before the test, how plausible the hypothesis is before the experiment. On the log-odds ruler it is literally a starting position, and Bayes' rule is then just one addition — posterior = prior + evidence. It is not optional: refusing to name a prior just means silently using 50/50, which for rare things is wildly wrong. Forgetting the prior is the base-rate fallacy — the reason a positive result from an excellent test for a rare condition still usually means you're fine.