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Bayesian nonparametric modelling of multiple graphs with an application to ethnic metabolic differences

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  • Marco Molinari
  • Andrea Cremaschi
  • Maria De Iorio
  • Nishi Chaturvedi
  • Alun D. Hughes
  • Therese Tillin

Abstract

We propose a novel approach to the estimation of multiple Gaussian graphical models (GGMs) to analyse patterns of association among a set of metabolites, under different conditions. Our motivating application is the SABRE (Southall And Brent REvisited) study, a triethnic cohort study conducted in the United Kingdom. Through joint modelling of pattern of association corresponding to different ethnic groups, we are able to identify potential ethnic differences in metabolite levels and associations, with the aim of gaining a better understanding of different risk of cardiometabolic disorders across ethnicities. We model the relationship between a set of metabolites and a set of covariates through a sparse seemingly unrelated regressions model and we use GGMs to represent the conditional dependence structure among metabolites. We specify a dependent generalised Dirichlet process prior on the edge inclusion probabilities to borrow strength across groups and we adopt the horseshoe prior to identify important biomarkers. Inference is performed via Markov chain Monte Carlo.

Suggested Citation

  • Marco Molinari & Andrea Cremaschi & Maria De Iorio & Nishi Chaturvedi & Alun D. Hughes & Therese Tillin, 2022. "Bayesian nonparametric modelling of multiple graphs with an application to ethnic metabolic differences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1181-1204, November.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:5:p:1181-1204
    DOI: 10.1111/rssc.12570
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    3. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    4. 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.
    5. Zhixiang Lin & Tao Wang & Can Yang & Hongyu Zhao, 2017. "On joint estimation of Gaussian graphical models for spatial and temporal data," Biometrics, The International Biometric Society, vol. 73(3), pages 769-779, September.
    6. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    7. T. Tony Cai & Hongzhe Li & Weidong Liu & Jichun Xie, 2013. "Covariate-adjusted precision matrix estimation with an application in genetical genomics," Biometrika, Biometrika Trust, vol. 100(1), pages 139-156.
    8. Christine Peterson & Francesco C. Stingo & Marina Vannucci, 2015. "Bayesian Inference of Multiple Gaussian Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 159-174, March.
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