Open Access
June 2014 Bayesian Adaptive Smoothing Splines Using Stochastic Differential Equations
Yu Ryan Yue, Daniel Simpson, Finn Lindgren, Håvard Rue
Bayesian Anal. 9(2): 397-424 (June 2014). DOI: 10.1214/13-BA866


The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that restrict the use of the smoothing spline in practical statistical work. Firstly, it becomes computationally prohibitive for large data sets because the number of basis functions roughly equals the sample size. Secondly, its global smoothing parameter can only provide a constant amount of smoothing, which often results in poor performances when estimating inhomogeneous functions. In this work, we introduce a class of adaptive smoothing spline models that is derived by solving certain stochastic differential equations with finite element methods. The solution extends the smoothing parameter to a continuous data-driven function, which is able to capture the change of the smoothness of the underlying process. The new model is Markovian, which makes Bayesian computation fast. A simulation study and real data example are presented to demonstrate the effectiveness of our method.


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Yu Ryan Yue. Daniel Simpson. Finn Lindgren. Håvard Rue. "Bayesian Adaptive Smoothing Splines Using Stochastic Differential Equations." Bayesian Anal. 9 (2) 397 - 424, June 2014.


Published: June 2014
First available in Project Euclid: 26 May 2014

zbMATH: 1327.62234
MathSciNet: MR3217001
Digital Object Identifier: 10.1214/13-BA866

Keywords: adaptive smoothing , Markov chain Monte Carlo , smoothing spline , Stochastic differential equation

Rights: Copyright © 2014 International Society for Bayesian Analysis

Vol.9 • No. 2 • June 2014
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