Abstract #300534

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JSM 2003 Abstract #300534
Activity Number: 205
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300534
Title: Spatially Adaptive Bayesian Regression Splines
Author(s): Veerabhadran Baladandayuthapani*+ and Bani K. Mallick and Raymond J. Carroll
Companies: Texas A&M University and Texas A&M University and Texas A&M University
Address: 301 Ball St., College Station, TX, 77840-1574,
Keywords: additive models ; Bayesian methods ; locally adaptive smoothing parameters ; Markov chain Monte Carlo ; mixed models ; variance models
Abstract:

We study penalized regression splines (P-splines), which are low-order basis function splines with a penalty to avoid undersmoothing. Such P-splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. While frequentist methods are available to address this issue, no Bayesian techniques have been developed. Our approach is to model the penalty parameter inherent in the P-spline method as a heteroscedastic regression function. We develop a full Bayesian hierarchical structure to do this. The method is extended to additive models with simultaneous spline based penalty functions for the unknown functions. In simulations, the method performs comparably to the current best frequentist P-spline method in terms of frequentist mean squared error, and better than some of the other Bayesian methods.

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