On the Bernstein-von Mises theorem for the Dirichlet process

Abstract

We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions of bounded variation, we strengthen this result to hold for all real numbers. This last result is proved via an explicit strong approximation coupling inequality.

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Cited by in corpus (2)

• Semiparametric Bayesian causal inference
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime