IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p218-d484966.html
   My bibliography  Save this article

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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Byron Botha & Rulof Burger & Kevin Kotzé & Neil Rankin & Daan Steenkamp, 2023. "Big data forecasting of South African inflation," Empirical Economics, Springer, vol. 65(1), pages 149-188, July.
    7. 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.
    8. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. 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.
    10. 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.
    11. 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).
    12. Ouyang, Jiarong & Cao, Xuan, 2024. "Consistent skinny Gibbs in probit regression," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    13. 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).
    14. 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.
    15. Jack Jewson & Li Li & Laura Battaglia & Stephen Hansen & David Rossell & Piotr Zwiernik, 2022. "Graphical model inference with external network data," CeMMAP working papers 20/22, Institute for Fiscal Studies.
    16. Qifan Song & Faming Liang, 2015. "High-Dimensional Variable Selection With Reciprocal L 1 -Regularization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1607-1620, December.
    17. Qifan Song & Guang Cheng, 2020. "Bayesian Fusion Estimation via t Shrinkage," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-385, August.
    18. Rahi Jain & Wei Xu, 2021. "HDSI: High dimensional selection with interactions algorithm on feature selection and testing," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-17, February.
    19. Li Ma, 2015. "Scalable Bayesian Model Averaging Through Local Information Propagation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 795-809, June.
    20. Gao Wang & Abhishek Sarkar & Peter Carbonetto & Matthew Stephens, 2020. "A simple new approach to variable selection in regression, with application to genetic fine mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1273-1300, December.

    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.