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Inferring network structure in non†normal and mixed discrete†continuous genomic data

Author

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  • Anindya Bhadra
  • Arvind Rao
  • Veerabhadran Baladandayuthapani
Abstract
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high†dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non†normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Anindya Bhadra & Arvind Rao & Veerabhadran Baladandayuthapani, 2018. "Inferring network structure in non†normal and mixed discrete†continuous genomic data," Biometrics, The International Biometric Society, vol. 74(1), pages 185-195, March.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:1:p:185-195
    DOI: 10.1111/biom.12711
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    References listed on IDEAS

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    1. 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.
    2. Shizhe Chen & Daniela M. Witten & Ali Shojaie, 2015. "Selection and estimation for mixed graphical models," Biometrika, Biometrika Trust, vol. 102(1), pages 47-64.
    3. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    4. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
    5. Michael Pitt & David Chan & Robert Kohn, 2006. "Efficient Bayesian inference for Gaussian copula regression models," Biometrika, Biometrika Trust, vol. 93(3), pages 537-554, September.
    6. Khatri, C. G. & Rao, C. Radhakrishna, 1976. "Characterizations of multivariate normality. I. Through independence of some statistics," Journal of Multivariate Analysis, Elsevier, vol. 6(1), pages 81-94, March.
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    Cited by:

    1. Yang Ni & Veerabhadran Baladandayuthapani & Marina Vannucci & Francesco C. Stingo, 2022. "Bayesian graphical models for modern biological applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 197-225, June.
    2. Yang Ni & Veerabhadran Baladandayuthapani & Marina Vannucci & Francesco C. Stingo, 2022. "Rejoinder to the discussion of “Bayesian graphical models for modern biological applications”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 287-294, June.
    3. Anindya Bhadra, 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 235-239, June.

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