IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p218-d484966.html

Bayesian Variable Selection with Applications in Health Sciences

Author

Listed:
  • Gonzalo García-Donato

    (Department of Economics and Finance, Universidad de Castilla-La Mancha, 02006 Albacete, Spain)

  • María Eugenia Castellanos

    (Department of Informatics and Statistics, Universidad Rey Juan Carlos, 28933 Mostoles, Spain)

  • Alicia Quirós

    (Department of Mathematics, Universidad de León, 24071 León, Spain)

Abstract

In health sciences, identifying the leading causes that govern the behaviour of a response variable is a question of crucial interest. Formally, this can be formulated as a variable selection problem. In this paper, we introduce the basic concepts of the Bayesian approach for variable selection based on model choice, emphasizing the model space prior adoption and the algorithms for sampling from the model space and for posterior probabilities approximation; and show its application to two common problems in health sciences. The first concerns a problem in the field of genetics while the second is a longitudinal study in cardiology. In the context of these applications, considerations about control for multiplicity via the prior distribution over the model space, linear models in which the number of covariates exceed the sample size, variable selection with censored data, and computational aspects are discussed. The applications presented here also have an intrinsic statistical interest as the proposed models go beyond the standard general linear model. We believe this work will broaden the access of practitioners to Bayesian methods for variable selection.

Suggested Citation

  • Gonzalo García-Donato & María Eugenia Castellanos & Alicia Quirós, 2021. "Bayesian Variable Selection with Applications in Health Sciences," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:218-:d:484966
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/218/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/218/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. James O. Berger & German Molina, 2005. "Posterior model probabilities via path‐based pairwise priors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 3-15, February.
    3. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    4. Veronika Ročková & Edward I. George, 2014. "EMVS: The EM Approach to Bayesian Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 828-846, June.
    5. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    6. Anabel Forte & Gonzalo Garcia‐Donato & Mark Steel, 2018. "Methods and Tools for Bayesian Variable Selection and Model Averaging in Normal Linear Regression," International Statistical Review, International Statistical Institute, vol. 86(2), pages 237-258, August.
    7. Veronika Ročková & Edward I. George, 2018. "The Spike-and-Slab LASSO," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 431-444, January.
    8. James Berger & M. J. Bayarri & L. R. Pericchi, 2014. "The Effective Sample Size," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 197-217, June.
    9. Loann D. Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," AMSE Working Papers 1852, Aix-Marseille School of Economics, France.
    10. Chris T. Volinsky & Adrian E. Raftery, 2000. "Bayesian Information Criterion for Censored Survival Models," Biometrics, The International Biometric Society, vol. 56(1), pages 256-262, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    2. Jieun Lee & Gyuhyeong Goh, 2024. "A hybrid deterministic–deterministic approach for high-dimensional Bayesian variable selection with a default prior," Computational Statistics, Springer, vol. 39(3), pages 1659-1681, May.
    3. M. Marsman & K. Huth & L. J. Waldorp & I. Ntzoufras, 2022. "Objective Bayesian Edge Screening and Structure Selection for Ising Networks," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 47-82, March.
    4. Buarque Andrade, Laura & Frenzel, Max & Bookhagen, Britta & Kresse, Carolin & Schmidt, Michael & Nassar, Nedal & Alonso, Elisa & Shojaeddini, Ensieh & Sandmann, Dirk, 2024. "From exploration to production: Understanding the development dynamics of lithium mining projects," Resources Policy, Elsevier, vol. 99(C).
    5. Eduardo Correia & Rodrigo Calili & José Francisco Pessanha & Maria Fatima Almeida, 2023. "Definition of Regulatory Targets for Electricity Non-Technical Losses: Proposition of an Automatic Model-Selection Technique for Panel Data Regressions," Energies, MDPI, vol. 16(6), pages 1-22, March.
    6. Fakhri J. Hasanov & Muhammad Javid & Frederick L. Joutz, 2022. "Saudi Non-Oil Exports before and after COVID-19: Historical Impacts of Determinants and Scenario Analysis," Sustainability, MDPI, vol. 14(4), pages 1-38, February.
    7. Kimia Keshanian & Daniel Zantedeschi & Kaushik Dutta, 2022. "Features Selection as a Nash-Bargaining Solution: Applications in Online Advertising and Information Systems," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2485-2501, September.
    8. Xiangyu Shi & Xiangyang Xu & Ruiyuan Cao & Tianfa Xie, 2026. "Bayesian variable selection and estimation based on asymmetric squared loss in high dimensions," Computational Statistics, Springer, vol. 41(1), pages 1-30, January.
    9. Davide Altomare & Guido Consonni & Luca La Rocca, 2013. "Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non-Local Priors," Biometrics, The International Biometric Society, vol. 69(2), pages 478-487, June.
    10. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Berndt Jesenko & Christian Schlögl, 2021. "The effect of web of science subject categories on clustering: the case of data-driven methods in business and economic sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(8), pages 6785-6801, August.
    12. Hong, Hyokyoung G. & Zheng, Qi & Li, Yi, 2019. "Forward regression for Cox models with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 268-290.
    13. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    14. Entong Gao & Jialu Guo & Xipeng Pang & Danya Bo & Zhe Chen, 2024. "Exploring pathways to comprehension performance in multilanguage smart voice systems: insights from Lasso regression, SEM, PLS-SEM, CNN, and BiLSTM," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 11(1), pages 1-20, December.
    15. Mukhtarov, Shahriyar & Mikayilov, Jeyhun I., 2023. "Could financial development eliminate energy poverty through renewable energy in Poland?," Energy Policy, Elsevier, vol. 182(C).
    16. Ouyang, Jiarong & Cao, Xuan, 2024. "Consistent skinny Gibbs in probit regression," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    17. Fouskakis, Dimitris & Ntzoufras, Ioannis & Perrakis, Konstantinos, 2020. "Variations of power-expected-posterior priors in normal regression models," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    18. Zhu, Jiangong & Weng, Wenyuan & You, Heze & Zhang, Jie & Wang, Yixiu & Jiang, Bo & Ji, Chenzhen & Wei, Xuezhe & Dai, Haifeng, 2025. "Lithium-ion battery end of life prediction based on the decelerating aging point," Applied Energy, Elsevier, vol. 401(PA).
    19. Latouche, Pierre & Mattei, Pierre-Alexandre & Bouveyron, Charles & Chiquet, Julien, 2016. "Combining a relaxed EM algorithm with Occam’s razor for Bayesian variable selection in high-dimensional regression," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 177-190.
    20. Jewson, Jack & Li, Li & Battaglia, Laura & Hansen, Stephen & Rossell, David & Zwiernik, Piotr, 2022. "Graphical model inference with external network data," CEPR Discussion Papers 17638, Centre for Economic Policy Research.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:218-:d:484966. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.