Consistency of Bayes estimates for nonparametric regression: normal theory

Performance characteristics of Bayes estimates are studied. More exactly, f or each subject in a data set, let xi be a vector of binary covariates and let Y be a normal response variable, with E{y\xi} = f(xi) and var {Y\xi} = 1. Here, f is an unknown function to be estimated from the data; the subjec ts are independent and identically distributed. Define a prior distribution on f as Sigma(k)w(k)pi(k)/Sigma(k)w(k), where pi(k) is Standard normal on the set of f which only depend on the first k covariates and w(k) > 0 for i nfinitely many k. Bayes estimates are consistent for all f. On the other ha nd if the pi(k) are flat, inconsistency is the rule.