Strong consistency in stochastic regression models via posterior covariance matrices

Abstract

In this paper we use posterior covariance matrices to study the strong consistency of Bayes estimators in stochastic regression models under various assumptions on the stochastic regressors. The random errors are assumed to form a martingale difference sequence. Several results are obtained using a recursion satisfied by the sequence of posterior covariance matrices. These results suggest that the posterior covariance matrix is a useful tool in studying strong consistency problems in stochastic regression models. Three examples from sequential design and adaptive control are discussed.