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

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.