bayes-estimator-admissible-squared-error
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-5.md
Created 2026-08-25T02:58:44+00:00
Under squared-error loss, every Bayes estimator with a proper prior is admissible, though exceptions exist for incomplete classes and 0–1 loss contexts.
Summary
If you are estimating a quantity and your goal is to minimize squared error, then the Bayes estimator backed by a well-defined prior is guaranteed to be the best you can do: no other estimator will beat it uniformly across all possible true values. This gives a solid theoretical reason to trust Bayesian estimation in standard prediction and fitting tasks, as long as the prior is proper and the loss is squared error rather than some other form.