Asymptotic normality of posterior in consistent Bayesian learning

摘要

This paper presents the study of asymptotic normality of posterior in Bayesian learning from the point of view of computational learning theory. Three reduced regular conditions, which are more convenient to be used than Walker's and Heyde's, are presented. The theorem, which shows under certain regular condition the poster distribution is not only consistent, but also approximately normal, is proved. Since the computation of normal distribution is relatively simpler, then the results can become the theoretic foundation for further study, for instance, assigning results prior distribution and simplifying the computation in Bayesian learning.