Bayesian Nonparametric Regression: Smoothing Using Gibbs Sampling
Oct 27 1993
This article discussed a Markov Chain-Monto Carlo approach to non-parametric regression. Both univariate and multivariate cases are considered. In the univariate case, the regression function is assumed to be a sample from a Gaussian process with suitably chosen mean and covariance functions. In the multivariate case, the regression surface is assumed to heave an additive structure with the components being univariate functions of each coordinate. It is further assumed that component functions are realizations from one-dimensional independent Gaussian process priors. The regression surface is the sum of these realizations. Under a quadratic loss function, the Bayes estimate is the mean of the posterior process. The posterior distributions are obtained by Gibbs sampling. Example are given where the coordinate functions are estimated by using cubic spline smoothers and smoothing parameters are estimated by their posterior distributions.
Keywords:Bayesian inference, nonparametric regression, generalized additive models, multiple smoothing parameter estimation, Gibbs sampling