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Bayesian graphical regression. (English) Zbl 1418.62088

Summary: 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.

MSC:

62F15 Bayesian inference
62G05 Nonparametric estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

EMVS; SemiPar
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Full Text: DOI Link

References:

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