STRONG CONSISTENCY IN STOCHASTIC REGRESSION-MODELS VIA POSTERIOR COVARIANCE MATRICES

In this paper Ne 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 a re assumed to form a martingale difference sequence. Several results a re obtained using a recursion satisfied by the sequence of posterior c ovariance matrices. These results suggest that the posterior covarianc e matrix is a useful tool in studying strong consistency problems in s tochastic regression models. Three examples from sequential design and adaptive control are discussed.