bernstein-von-mises-gaussian-convergence
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-2.md
Created 2026-08-25T02:58:43+00:00
The Bernstein-von Mises theorem states that under regularity conditions, the posterior distribution converges to a Gaussian as nāā, independent of the chosen prior.
Summary
With enough data, a Bayesian analysis settles into a predictable bell-shaped pattern no matter what starting assumptions you made, so your initial guesses wash out and the result becomes robust. This matters because it means different analysts or systems who disagree on priors will still converge to the same answer at scale, and the uncertainty they report takes a simple, well-understood form that is easy to reason about.