摘要：We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regression function and efficient, $\sqrt{n-consistent estimation of the error standard deviation.
关键词：Nonparametric regression;Bayesian inference, estimation of error variance;semiparametric Bernstein-von Mises.
