Bayesian Graphical Regression

• Published in: Journal of the American Statistical Association Vol. 114; no. 525; pp. 184 - 197
• Main Authors: Ni, Yang, Stingo, Francesco C., Baladandayuthapani, Veerabhadran
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 02.01.2019; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Bayesian theory; Cancer; Computer simulation; Dependence; Directed acyclic graph; equations; gene regulatory networks; Genomics; Graph theory; Graphs; Modelling; Myeloma; Nonlocal prior; Precision medicine; Predictive network; Regression analysis; Simulation; Specification; Statistical methods; Statistics; Subject-specific graph; Theory and Methods; Varying graph structure; Predictive network; Directed acyclic graph; Varying graph structure; Subject-specific graph; Non-local prior
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2017.1389739

We consider the problem of modeling conditional independence structures in heterogenous data in the presence of additional subject-level covariates-termed graphical regression. We propose a novel specification of a conditional (in)dependence function of covariates-which allows the structure of a directed graph to vary flexibly with the covariates; imposes sparsity in both edge and covariate selection; produces both subject-specific and predictive graphs; and is computationally tractable. We provide theoretical justifications of our modeling endeavor, in terms of graphical model selection consistency. We demonstrate the performance of our method through rigorous simulation studies. We illustrate our approach in a cancer genomics-based precision medicine paradigm, where-in we explore gene regulatory networks in multiple myeloma taking prognostic clinical factors into account to obtain both population-level and subject-level gene regulatory networks. Supplementary materials for this article are available online.