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Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo

Author

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  • Federico Castelletti

    (Università Cattolica del Sacro Cuore (Milan))

  • Guido Consonni

    (Università Cattolica del Sacro Cuore (Milan))

  • Luca Rocca

    (Università di Modena e Reggio Emilia)

Abstract

We contribute to the discussion of the paper by Ni et al. (Stat Methods Appl, 2021. https://doi.org/10.1007/s10260-021-00572-8 ) by focusing on two aspects: (i) ordering of the variables for directed acyclic graphical models, and (ii) heterogeneity of the data in the presence of covariates. With regard to (i) we claim that an ordering should be assumed only when strongly reliable prior information is available; otherwise one should proceed with an unspecified ordering to guard against order misspecification. Alternatively, one can carry out Bayesian inference on the space of Markov equivalence classes or use a blend of observational and interventional data to alleviate the lack of identification. With regard to (ii) we complement the Authors’ analysis by enlarging the scope to mixed graphs as well as nonparametric Bayesian models.

Suggested Citation

  • Federico Castelletti & Guido Consonni & Luca Rocca, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 261-267, June.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:2:d:10.1007_s10260-021-00601-6
    DOI: 10.1007/s10260-021-00601-6
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    References listed on IDEAS

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    1. Ntzoufras, Ioannis & Tarantola, Claudia, 2013. "Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 161-177.
    2. Min Jin Ha & Francesco Claudio Stingo & Veerabhadran Baladandayuthapani, 2021. "Bayesian Structure Learning in Multilayered Genomic Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 605-618, April.
    3. 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.
    4. Alain Hauser & Peter Bühlmann, 2015. "Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 291-318, January.
    5. Anindya Bhadra & Bani K. Mallick, 2013. "Joint High-Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis," Biometrics, The International Biometric Society, vol. 69(2), pages 447-457, June.
    6. Guido Consonni & Luca La Rocca & Stefano Peluso, 2017. "Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 741-764, September.
    7. Federico Castelletti & Guido Consonni, 2021. "Bayesian inference of causal effects from observational data in Gaussian graphical models," Biometrics, The International Biometric Society, vol. 77(1), pages 136-149, March.
    8. Federico Castelletti, 2020. "Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures," International Statistical Review, International Statistical Institute, vol. 88(3), pages 752-775, December.
    9. Federico Castelletti & Guido Consonni, 2020. "Discovering causal structures in Bayesian Gaussian directed acyclic graph models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1727-1745, October.
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