Bayesian adaptive smoothing splines using stochastic differential equations

Yu Ryan Yue, Daniel Simpson, Finn Lindgren, Håvard Rue

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)397-424
Number of pages28
Issue number2
StatePublished - 2014
Externally publishedYes


  • Adaptive smoothing
  • Markov chain monte carlo
  • Smoothing spline
  • Stochastic differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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