  The classical parametric and semiparametric Bernstein -- von Mises (BvM)
results are reconsidered in a non-classical setup allowing finite samples 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 \emph{critical dimension} $ p $ of the full parameter for which the BvM
result is applicable. In the important i.i.d. case, we show that the condition
"$ p^{3} / n $ is small" is sufficient for BvM result to be valid under general
assumptions on the model. We also provide an example of a model with the phase
transition effect: the statement of the BvM theorem fails when the dimension $
p $ approaches $ n^{1/3} $. The results are extended to the case of infinite
dimensional parameters with the nuisance parameter from a Sobolev class. In
particular we show near normality of the posterior if the smoothness parameter
$s$ exceeds 3/2.
