bayes-likelihood-vs-posterior-function
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-1.md
Created 2026-08-25T02:58:42+00:00
The likelihood P(E|H) is a function of the data E with the hypothesis H fixed, while the posterior P(H|E) is a function of the hypothesis H with the data E fixed.
Summary
The likelihood and the posterior look like mirror images, but they answer opposite questions: the likelihood asks "given my hypothesis, how surprising is this data?" while the posterior asks "given this data, how plausible is each hypothesis?" Keeping the fixed variable and the varying variable straight matters because mixing them up is exactly how people fall into the prosecutor's fallacy or misweight evidence in inference.