THE ASYMPTOTIC NORMALITY OF POSTERIOR IN BAYESIAN LEARNING

This paper studies the consistency and asymptotic normality of posterior in Bayesian learning.It presents a set of regular conditions for Bayesian learning,and proves that under these conditions Bayesian learning has not only consistency but also has normal distribution of posterior asymptotically.Because the computing of normal distribution is relatively simple,the results in this paper provide a theoretic basis for assessing resultful prior and methods to reduce the computing in Bayesian learning.The regular conditions presented in this paper are simpler than the 5 conditions given by Heyde and Johnstone,and more suitable for application.