ROBUST BAYESIAN ESTIMATION

Publisher Summary There is a considerable body of literature expounding that proper statistical behavior is to take a convenient but not necessarily true prior, compute the posterior, and act accordingly. This chapter describes the way in which much can be gained with little lost, at least in the case of estimating the mean of a univariate normal with known variance. The simple linear estimator has an infinite expected risk if the loss is squared error and the true prior has infinite variance. Even truncating the risk does not help much. The chapter discusses the concept of robustness from the behavioristic Bayes approach. It describes the calculation of the risks for the Bayes estimates for non-normal priors by numerical integration for certain values of θ, followed by numerical integration over θ.