Bayesian point estimation and prediction

Abstract

In the Bayesian viewpoint, point estimation and prediction are treated from a decision-making standpoint. If a loss function can be determined which associates a loss with every possible error of estimation or prediction, then the optimal estimator or predictor is that value which minimizes expected loss. In most applications, the loss function is assumed to be linear or quadratic in the error of estimation or prediction, although there are many practical situations in which these simple functions are quite inappropriate. In this paper, we investigate the properties of Bayesian point estimates under other loss functions; both the general case and two special cases (power and exponential loss functions) are considered. For the special cases, we also investigate the sensitivity of Bayesian point estimation and prediction to misspecification in the loss function and discuss the practical implications of the results. © 1974 Institute of Statistical Mathematics.