I am trying to understand asymptotic Normality of posterior distributuions. Specifically, what are the (regularity) conditions that allow us to use this approximation? The problem is that the references I could find online are very mathematical for me to understand clearly. For example the 11th chapter in the book by Hartigan (1983), Bayes Theory; or the paper by Walker (1969).
Please suggest some references to understand asymptotic Normality, for someone without rigorous background in Mathematics. I do have a good understanding of Probability theory.