bgsmtr

bgsmtr fits Bayesian group-sparse multi-task regression models to identify genetic associations with high-dimensional imaging phenotypes and other multivariate traits.

Key Features:

• Bayesian Hierarchical Modeling: Employs hierarchical priors and a structured group l2,1-norm penalty to induce sparsity at both gene and SNP levels.
• Three-level Gaussian Scale Mixture: Represents the model as a three-level Gaussian scale mixture to implement the hierarchical shrinkage structure.
• Gibbs Sampling for Posterior Inference: Uses Gibbs sampling to perform posterior simulations within the three-level Gaussian scale mixture representation.
• Full Posterior Inference and Credible Intervals: Provides full posterior inference, including construction of credible intervals for regression coefficients.
• Application to High-Dimensional Imaging Data: Demonstrated on neuroimaging datasets from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and supports phenotypes of dimension up to 100.
• Improved Statistical Coverage: Simulation studies report interval estimates with adequate coverage probabilities that outperform nonparametric bootstrap methods.
• Posterior Mode Correspondence: The posterior mode of the hierarchical model corresponds to the estimator proposed by Wang et al.

Scientific Applications:

• Neuroimaging Genomic Studies: Analyze genetic determinants of brain structure and function using neuroimaging phenotypes such as those from ADNI.
• Genetic Association Studies: Assess associations between SNPs and multivariate phenotypic traits to investigate complex trait heritability.

Methodology:

Implements a Bayesian group-sparse multi-task regression with hierarchical priors and a structured group l2,1-norm sparsity-inducing penalty at gene and SNP levels, represented as a three-level Gaussian scale mixture, and performs posterior simulation via Gibbs sampling (the posterior mode corresponds to the estimator of Wang et al.).