Abstract
Performance characteristics of Bayes estimates are studied. More exactly, for each subject in a data set, let ξ be a vector of binary covariates and let Y be a normal response variable, with E{Y|ξ}=f(ξ) and var{Y|ξ}=1. Here, f is an unknown function to be estimated from the data; the subjects are independent and identically distributed. Define a prior distribution on f as ∑kwkπk/∑kwk, where πk is standard normal on the set of f which only depend on the first k covariates and wk>0 for infinitely many k. Bayes estimates are consistent for all f. On the other hand, if the πk are flat, inconsistency is the rule.
Citation
Persi W. Diaconis. David Freedman. "Consistency of Bayes estimates for nonparametric regression: normal theory." Bernoulli 4 (4) 411 - 444, Dec 1998.
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