Spatially adaptive priors for regression and spatial modeling

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The smoothing splines and penalized regression splines (P-splines) are popular nonparametric regression methods for curve fitting problems, and the thin-plate spline (a two-dimensional version of smoothing spline) is a well-known surface fitting method and has been used intensively in spatial smoothing area. These spline basis methods, however, both suffer from having only one global smoothing parameter that controls the degrees of smoothness for the fit. It is especially an issue when the function of interest is highly varying through the input space. To overcome this inadequacy, we develop a class of priors for adaptive spline smoothing. These priors extend certain stochastic process by using a spatially adaptive variance component and taking a further process as prior for this variance function.