Large sample posterior normality of the population mean
H. D. Brunk, Donald A. Pierce · Communication in Statistics- Theory and Methods · 1977
For a very wide class of distributions in the multiparameter exponential family it is shown that the posterior distribution of the population mean μ is such that has asymptotically the standard normal distribution. It is suggested that this supports the validity of the usual large sample procedure for making inference about y when little is known about the form of the population. The convergence is obtained for any sequence of random samples of increasing size for which the first m sample moments are fixed at arbitrary values, for some specified m≥2.