Asymptotic Normality of Posterior Distributions for Exponential Families with211 Many Parameters

摘要

We study consistency and asymptotic normality of posterior distributions of the211u001enatural parameter for an exponential family when the dimension of the parameter 211u001egrows with the sample size. Under certain growth restrictions on the dimension, 211u001ewe show that the posterior distributions concentrate in neighborhoods of the true 211u001eparameter and can be approximated by an appropriate normal distribution.