Bayesian Smoothing Splines Using Stochastic Differential Equations

• Activity Number: 40
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yu Yue*+
• Companies: Baruch College

Abstract

Smoothing spline is one of the most popular curve-fitting methods, and its two-dimensional extension: thin-plate spline, has been one of the most prominent smoothers in spatial statistics research. However, there are two obstacles to the widespread adoption of smoothing spline smoothers in practical statistical work. First, they become computationally prohibitive for large data sets. Second, the global smoothing parameter only provides constant amount of smoothing, which often results in poor performances of smoothing splines when estimating spatially inhomogeneous functions.

In this talk, we introduce a class of smoothing spline models based on solving certain stochastic differential equations with finite element methods. The resulting solutions are the best finite dimensional representations to the continuous-time processes with fast computations. More importantly, there is no barrier - conceptual or computational - to extending them to more flexible adaptive smoothing splines. Furthermore, it is even possible to construct them on sphere and other manifolds. The simulated and real data examples will be presented to demonstrate the effectiveness of our method.