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Bayesian regression with multivariate linear splines

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  • C. C. Holmes
  • B. K. Mallick

Abstract

We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data.

Suggested Citation

  • C. C. Holmes & B. K. Mallick, 2001. "Bayesian regression with multivariate linear splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 3-17.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:1:p:3-17
    DOI: 10.1111/1467-9868.00272
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    Cited by:

    1. Matthew Wheeler & A. John Bailer, 2012. "Monotonic Bayesian Semiparametric Benchmark Dose Analysis," Risk Analysis, John Wiley & Sons, vol. 32(7), pages 1207-1218, July.
    2. Zhiyong Chen & Jianbao Chen, 2022. "Bayesian analysis of partially linear, single-index, spatial autoregressive models," Computational Statistics, Springer, vol. 37(1), pages 327-353, March.
    3. Wai-Yin Poon & Hai-Bin Wang, 2014. "Multivariate partially linear single-index models: Bayesian analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 755-768, December.
    4. Jamie L. Bigelow & David B. Dunson, 2007. "Bayesian Adaptive Regression Splines for Hierarchical Data," Biometrics, The International Biometric Society, vol. 63(3), pages 724-732, September.
    5. Wang, Hai-Bin, 2009. "Bayesian estimation and variable selection for single index models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2617-2627, May.
    6. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    7. Chiara Mazzetta & Steve Brooks & Stephen N. Freeman, 2007. "On Smoothing Trends in Population Index Modeling," Biometrics, The International Biometric Society, vol. 63(4), pages 1007-1014, December.
    8. Wesley K. Thompson & Ori Rosen, 2008. "A Bayesian Model for Sparse Functional Data," Biometrics, The International Biometric Society, vol. 64(1), pages 54-63, March.

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