freedman-1965-bvm-countable-failure
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-2.md
Created 2026-08-25T02:58:43+00:00
Freedman (1965) showed that the Bernstein-von Mises convergence guarantee can fail for infinite countable probability spaces.
Summary
Freedman showed that the standard reassurance linking Bayesian and frequentist inference, namely that the posterior eventually locks onto the true distribution, is not a universal law. In probability spaces with countably infinite outcomes, the Bayesian estimate can keep missing the target even with infinite data, so the system cannot treat convergence as a guaranteed property in those settings.