On Asymptotic Posterior Normality for Stochastic Processes

Summary Asymptotic normality of the posterior distribution of a parameter in a stochastic process is shown to hold under conditions which do little more than ensure consistency of a maximum likelihood estimator. Much more stringent conditions are required to ensure asymptotic normality of the MLE. This contrast, which has implications of considerable significance, does not emerge in the classical context of independent and identically distributed observations.