map-posterior-mean-symmetric-only
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-5.md
Created 2026-08-25T02:58:44+00:00
The MAP estimator (mode of the posterior) and the posterior mean coincide only for symmetric posterior distributions.
Summary
The "most likely value" and the "average of all plausible values" give the same answer only when the distribution of possibilities is perfectly balanced left and right. In practice this means that for any skewed or lopsided uncertainty, choosing the peak versus choosing the mean are genuinely different decisions, and the system must treat them as distinct rather than interchangeable.