MARS: Selecting basis functions and knots with an empirical Bayes method

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.

Original languageEnglish
Pages (from-to)583-597
Number of pages15
JournalComputational Statistics
Issue number4
Publication statusPublished - Dec 1 2007


  • Akaike Bayes information criterion
  • Estimation of interaction terms
  • Marginal likelihood
  • Multivariate adaptive regression
  • Penalized likelihood approach

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics


Dive into the research topics of 'MARS: Selecting basis functions and knots with an empirical Bayes method'. Together they form a unique fingerprint.

Cite this