STRONG CONSISTENCY OF BAYES ESTIMATES IN STOCHASTIC REGRESSION-MODELS

Under minimum assumptions on the stochastic regressors, strong consist ency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f. f of i.i.d. random errors is assumed to have finite Fisher informatio n I=integral(-infinity)(infinity) (f')(2)/f dx < infinity; (2) for gen eral priors, we assume f is strongly unimodal. The result can be consi dered as an application of a theorem of Doob to stochastic regression models. (C) 1996 Academic Press. Inc.