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August 1999 Wald Lecture: On the Bernstein-von Mises theorem with infinite-dimensional parameters
David Freedman
Ann. Statist. 27(4): 1119-1141 (August 1999). DOI: 10.1214/aos/1017938917


If there are many independent, identically distributed observations governed by a smooth, finite-dimensional statistical model, the Bayes estimate and the maximum likelihood estimate will be close. Furthermore, the posterior distribution of the parameter vector around the posterior mean will be close to the distribution of the maximum likelihood estimate around truth. Thus, Bayesian confidence sets have good frequentist coverage properties, and conversely. However, even for the simplest infinite-dimensional models, such results do not hold. The object here is to give some examples.


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David Freedman. "Wald Lecture: On the Bernstein-von Mises theorem with infinite-dimensional parameters." Ann. Statist. 27 (4) 1119 - 1141, August 1999.


Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0957.62002
MathSciNet: MR1740119
Digital Object Identifier: 10.1214/aos/1017938917

Primary: 62A15
Secondary: 62C15

Keywords: asymptotic confidence sets , Bayesian inference , consistency , Gaussian priors

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • August 1999
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