Source: Ann. Statist.
Volume 27, Number 4
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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