Bayesian structure learning in sparse Gaussian graphical models. Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence of variables through the presence or absence of edges in the underlying graph. In this paper, we introduce a novel and efficient Bayesian framework for Gaussian graphical model determination which is a trans-dimensional Markov Chain Monte Carlo (MCMC) approach based on a continuous-time birth-death process. We cover the theory and computational details of the method. It is easy to implement and computationally feasible for high-dimensional graphs. We show our method outperforms alternative Bayesian approaches in terms of convergence, mixing in the graph space and computing time. Unlike frequentist approaches, it gives a principled and, in practice, sensible approach for structure learning. We illustrate the efficiency of the method on a broad range of simulated data. We then apply the method on large-scale real applications from human and mammary gland gene expression studies to show its empirical usefulness. In addition, we implemented the method in the R package BDgraph which is freely available at url{}.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Donald Williams; Joris Mulder: BGGM: Bayesian Gaussian Graphical Models in R (2020) not zbMATH
  2. Li, Zehang Richard; McComick, Tyler H.; Clark, Samuel J.: Using Bayesian latent Gaussian graphical models to infer symptom associations in verbal autopsies (2020)
  3. Mohammadi, Reza; Pratola, Matthew; Kaptein, Maurits: Continuous-time birth-death MCMC for Bayesian regression tree models (2020)
  4. Mulgrave, Jami J.; Ghosal, Subhashis: Bayesian inference in nonparanormal graphical models (2020)
  5. Ni, Yang; Müller, Peter; Ji, Yuan: Bayesian double feature allocation for phenotyping with electronic health records (2020)
  6. Ayyıldız, Ezgi; Purutçuoğlu, Vilda; Weber, Gerhard Wilhelm: Loop-based conic multivariate adaptive regression splines is a novel method for advanced construction of complex biological networks (2018)
  7. Dobra, Adrian; Mohammadi, Reza: Loglinear model selection and human mobility (2018)
  8. Leppä-aho, Janne; Pensar, Johan; Roos, Teemu; Corander, Jukka: Learning Gaussian graphical models with fractional marginal pseudo-likelihood (2017)
  9. Mohammadi, A.; Wit, E. C.: Bayesian structure learning in sparse Gaussian graphical models (2015)
  10. Mohammadi, A.; Wit, E.C.: BDgraph: An R Package for Bayesian Structure Learning in Graphical Models (2015) arXiv
  11. Pircalabelu, Eugen; Claeskens, Gerda; Jahfari, Sara; Waldorp, Lourens J.: A focused information criterion for graphical models in fMRI connectivity with high-dimensional data (2015)