improper-prior-can-yield-proper-posterior
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-5.md
Created 2026-08-25T02:58:44+00:00
An improper prior can sometimes yield a proper posterior, but not always; the posterior must still be proper for Bayesian inference to be valid.
Summary
Starting with a prior that is not a valid probability distribution (an "improper" prior) can still produce a usable posterior, but it is not guaranteed to work out, so the result must be checked. If the posterior turns out to be improper, the entire Bayesian inference is invalid and any conclusions drawn from it cannot be trusted.