Abstract
If there are many independent, identically distributed\nobservations governed by a smooth, finite-dimensional statistical model, the\nBayes estimate and the maximum likelihood estimate will be close. Furthermore,\nthe posterior distribution of the parameter vector around the posterior mean\nwill be close to the distribution of the maximum likelihood estimate around\ntruth. Thus, Bayesian confidence sets have good frequentist coverage\nproperties, and conversely. However, even for the simplest infinite-dimensional\nmodels, such results do not hold. The object here is to give some examples.
Keywords
Frequentist inferenceMathematicsMaximum likelihoodvon Mises distributionApplied mathematicsBayes' theoremPosterior probabilityLikelihood principleIndependent and identically distributed random variablesBayesian probabilityDistribution (mathematics)Statisticsvon Mises yield criterionLikelihood functionMathematical analysisBayesian inferenceRandom variableQuasi-maximum likelihoodPhysicsFinite element method
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Publication Info
- Year
- 1999
- Type
- article
- Volume
- 27
- Issue
- 4
- Citations
- 142
- Access
- Closed
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Cite This
David A. Freedman
(1999).
Wald Lecture: On the Bernstein-von Mises theorem with infinite-dimensional parameters.
The Annals of Statistics
, 27
(4)
.
https://doi.org/10.1214/aos/1017938917
Identifiers
- DOI
- 10.1214/aos/1017938917