The Bernstein–von Mises theorem and nonregular models
Bernstein–von Mises 定理与非正则模型
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the “true” solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and that the posterior distribution has not only Gaussian components as in the case of regular models (the Bernstein–von Mises theorem) but also has Gamma distribution components whose form depends on the behaviour of the prior distribution…