Chapter VIII - The MSE for Incorrect Prior Assumptions

Abstract

This chapter focuses on the mean square error (MSE) for incorrect prior assumptions. A strong and serious but valid criticism of Bayesian methods is that the prior information they depend on may not be correct. In the context of the development of the estimators, the form of the incorrect prior assumptions for the Bayes, mixed, and minimax estimators respectively, are an incorrectly specified mean vector and/or incorrectly specified dispersion matrix, an incorrect stochastic prior information, and an incorrect ellipsoid. The chapter highlights the MSE of the Bayes estimator (BE). The MSE of an estimator derived from the incorrect prior assumptions is not uniformly less than that of the least square estimator when averaged over correct prior assumptions. The chapter describes the corresponding comparisons of the MSE of the mixed estimator to the least square (LS) estimator when the mean and dispersion of Φ is misspecified and the correspondence between incorrect prior assumptions for a BE and a mixed estimator.