wald-admissibility-theorem

IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-3.md

Created 2026-08-25T02:58:43+00:00

Wald's Admissibility Theorem states that every unique Bayesian procedure is admissible, and every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

Summary

This result shows that the family of "sensible" statistical decision rules—ones that no other rule beats across every possible scenario—is essentially the same family you get by applying Bayesian reasoning, or by taking limits of Bayesian methods. In practice, it means the choice between Bayesian and frequentist frameworks is less about which produces valid answers and more about how you want to structure the problem, since both routes converge on the same set of reasonable strategies.