Аннотация:
The classical results of an asymptotic normality of the posterior distribution (Bernstein - von Mises theorem) will be reconsidered in a non-classical setup allowing finite samples, high parameter dimension and model misspecification. In the case of a finite dimensional nuisance parameter we obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the nuisance and target parameters. This helps to identify the so called critical dimension of the full parameter for which the BvM result is applicable. The results are extended to the case of infinite dimensional parameter families from a Sobolev class.
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