Early Highlights in the History of the Bernstein-von Mises Theorem

TL;DR

This paper reviews the historical development of the Bernstein-von Mises theorem, highlighting key contributions from Laplace to Le Cam and uncovering previously obscure sources.

Contribution

It provides a comprehensive historical overview of the theorem's evolution, emphasizing overlooked early works and their influence on modern Bayesian asymptotics.

Findings

Tracing the theorem's origins from Laplace to Le Cam

Uncovering previously unknown historical sources

Clarifying the theorem's development and applications

Abstract

The designation ``Bernstein-von Mises theorem'' is apparently due to Lucien Le Cam. Roughly, the assertion of this theorem states that the posterior distribution of a parameter, conditioned on a large sample, is approximately normal, independent of a particular prior. The present paper discusses important steps in the development of this theorem and its applications, from Laplace in 1774 to Le Cam in 1953. Regarding Bernstein and his disciple Neyman, it thereby relies on sources which were widely unknown and hard to obtain until recently.