We consider Bayesian asymptotics for these problems. When the dimension of the parameter space grows with the sample size, approximation of the posterior distribution is a much more difficult task. Under certain restrictions on the growth rate of the dimension, a normal approximation can still be expected. Results in this direction has been established for the regression problem , generalized linear models and for exponential families . Concentration of posterior in neghbourhoods of certain sizes around the true value of the parameter or the asymptotic equivalence of Bayes estimates and the maximum likelihood estimate is also concluded under appropriate conditions.
Work is still in progress for situations similar to the three cases mentioned above.