Bayesian Variable Selection in Multivariate Nonlinear Regression with Graph Structures

2020/10/27 by Yabo Niu, Niu, Yabo, Nilabja Guha +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Metabolomics and Mass Spectrometry Studies #Methodology (stat.ME) #Spectroscopy and Chemometric Analyses #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2010.14638

openalex publication_date 2020/10/27 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28

Abstract

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.

Citations

• Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models

Cited by

• Spatially Varying Gene Regulatory Networks via Bayesian Nonparametric Covariate-Dependent Directed Cyclic Graphical Models

Related

• Bayesian Estimation of Gaussian Graphical Models with Predictive Covariance Selection
• Fast Bayesian High-Dimensional Gaussian Graphical Model Estimation
• Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures
• Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection
• Bayesian Estimation for Gaussian Graphical Models: Structure Learning, Predictability, and Network Comparisons