Abstract: It was well established by Wahba (1978) that a smoothing spline procedure is equivalent to a Bayesian procedure under a partially improper prior. Based on this interpretation, statistical inference other than point estimation was made possible for smoothing spline estimators of a Gaussian regression function (Wahba (1983)). This article extends Wahba's results to non-Gaussian regression problems via a simple approximation known as Laplace's method. The results make the Bayesian inference tools developed for Gaussian models applicable to non-Gaussian models.
Key words and phrases: Bayesian confidence interval, Laplace's method, posterior analysis, smoothing spline.