Bernstein - von Mises Theorem for quasi-posterior

Bernstein - von Mises Theorem is one of the most remarkable result in Bayesian inference. It claims that under rather weak conditions on the model and on the prior, the posterior distribution is asymptotically close to a normal distribution with the mean at the MLE and the covariance matrix which is inverse of the total Fisher information matrix.This talk extends this result to the situation when the likelihood function is possibly misspecified, the sample size is fixed and does not tend to infinity, and the parameter dimension is large relative to sample size. A further extension to hyperpriors and Bayesian model selection is discussed as well.