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Bayesian monotone regression using Gaussian process projection

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  • Lizhen Lin
  • David B. Dunson

Abstract

Shape-constrained regression analysis has applications in dose-response modelling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid implausible results. We propose a novel method, focusing on monotone curve and surface estimation, which uses Gaussian process projections. Our inference is based on projecting posterior samples from the Gaussian process. We develop theory on continuity of the projection and rates of contraction. Our approach leads to simple computation with good performance in finite samples. The proposed projection method can also be applied to other constrained-function estimation problems, including those in multivariate settings.

Suggested Citation

  • Lizhen Lin & David B. Dunson, 2014. "Bayesian monotone regression using Gaussian process projection," Biometrika, Biometrika Trust, vol. 101(2), pages 303-317.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:2:p:303-317.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast063
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    Cited by:

    1. Lee, Kwangmin & Lee, Jaeyong, 2023. "Post-processed posteriors for sparse covariances," Journal of Econometrics, Elsevier, vol. 236(1).
    2. Zhao, Yanyun, 2015. "Bayesian Linear Regression with Conditional Heteroskedasticity," DES - Working Papers. Statistics and Econometrics. WS ws1504, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Yang Liu & Xiaojing Wang, 2020. "Bayesian Nonparametric Monotone Regression of Dynamic Latent Traits in Item Response Theory Models," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 274-296, June.
    4. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.
    5. Taeryon Choi & Hea-Jung Kim & Seongil Jo, 2016. "Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2751-2771, November.
    6. Rohit Singh & Santosh Singh Rathore, 2022. "Linear and non-linear bayesian regression methods for software fault prediction," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(4), pages 1864-1884, August.
    7. Patrick Link & Miltiadis Poursanidis & Jochen Schmid & Rebekka Zache & Martin Kurnatowski & Uwe Teicher & Steffen Ihlenfeldt, 2022. "Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing," Journal of Intelligent Manufacturing, Springer, vol. 33(7), pages 2129-2142, October.
    8. repec:cte:whrepe:ws1504 is not listed on IDEAS

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