Strong Consistency of Bayes Estimates in Stochastic Regression Models

Under minimum assumptions on the stochastic regressors, strong consistency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f.fof i.i.d. random errors is assumed to have finite Fisher informationI=∫∞−∞(f′)2/f dx<∞; (2) for general priors, we assumefis strongly unimodal. The result can be considered as an application of a theorem of Doob to stochastic regression models.