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Fast Bayesian model assessment for nonparametric additive regression

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  • McKay Curtis, S.
  • Banerjee, Sayantan
  • Ghosal, Subhashis

Abstract

Variable selection techniques for the classical linear regression model have been widely investigated. Variable selection in fully nonparametric and additive regression models has been studied more recently. A Bayesian approach for nonparametric additive regression models is considered, where the functions in the additive model are expanded in a B-spline basis and a multivariate Laplace prior is put on the coefficients. Posterior probabilities of models defined by selection of predictors in the working model are computed, using a Laplace approximation method. The prior times the likelihood is expanded around the posterior mode, which can be identified with the group LASSO, for which a fast computing algorithm exists. Thus Markov chain Monte-Carlo or any other time consuming sampling based methods are completely avoided, leading to quick assessment of various posterior model probabilities. This technique is applied to the high-dimensional situation where the number of parameters exceeds the number of observations.

Suggested Citation

  • McKay Curtis, S. & Banerjee, Sayantan & Ghosal, Subhashis, 2014. "Fast Bayesian model assessment for nonparametric additive regression," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 347-358.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:347-358
    DOI: 10.1016/j.csda.2013.05.012
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    3. Yuan, Ming & Lin, Yi, 2005. "Efficient Empirical Bayes Variable Selection and Estimation in Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1215-1225, December.
    4. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Howard D. Bondell & Brian J. Reich, 2008. "Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR," Biometrics, The International Biometric Society, vol. 64(1), pages 115-123, March.
    7. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    11. Sally Wood & Robert Kohn & Tom Shively & Wenxin Jiang, 2002. "Model selection in spline nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 119-139, January.
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    Cited by:

    1. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    2. Xu, Bin & Lin, Boqiang, 2015. "How industrialization and urbanization process impacts on CO2 emissions in China: Evidence from nonparametric additive regression models," Energy Economics, Elsevier, vol. 48(C), pages 188-202.
    3. Xu, Bin & Lin, Boqiang, 2016. "Reducing CO2 emissions in China's manufacturing industry: Evidence from nonparametric additive regression models," Energy, Elsevier, vol. 101(C), pages 161-173.

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