Approximate bayes estimators for stochastic processes

Abstract

Let 8, be an estimaJor of a parameter 8 based on observing a stochastic process over a time period of length T. Suppose is asymptotically normally distributed as T + 30. Given a prior distribution on 8, we propose constructing a posterior distribution based on this asymptotic normal likelihood. Call the mean of this posterior an approximate Bayes estimator. We give conditions under which this estimator is strongly consistent and investigate its performance in reducing mean square error for a birth and death process and a branching process.