Bernstein-von Mises theorem for log-concave posteriors
Statistics Theory
2026-02-12 v1 Statistics Theory
Abstract
We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of Bernstein-von Mises theorem, our versions do not require technical smoothness assumptions, and they solely rely on convex analysis.
Cite
@article{arxiv.2602.10256,
title = {Bernstein-von Mises theorem for log-concave posteriors},
author = {Victor-Emmanuel Brunel},
journal= {arXiv preprint arXiv:2602.10256},
year = {2026}
}