Joint High‐Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis

: We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high‐dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an ass...

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Bibliographic Details
Published in:Biometrics 2013-06, Vol.69 (2), p.447-457
Main Authors: Bhadra, Anindya, Mallick, Bani K
Format: Article
Language:eng ; fre
Subjects:
5' Untranslated Regions
Bayes Theorem
Bayesian analysis
Bayesian theory
BIOMETRIC METHODOLOGY
biometry
Biometry - methods
Biostatistics
Computer Simulation
correlated responses
covariance
eQTL Analysis
Gaussian graphical model
gene expression
Gene Expression Profiling - statistics & numerical data
Genomics
HapMap Project
Humans
Hyper-inverse Wishart distribution
Joint variable and covariance selection
Likelihood Functions
Markov Chains
Models, Statistical
Monte Carlo Method
Multivariate Analysis
Polymorphism, Single Nucleotide
Quantitative Trait Loci
Regression Analysis
single nucleotide polymorphism
Sparse seemingly unrelated regression
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Summary:: We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high‐dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an association analysis between the high‐dimensional sets of predictors and responses in such a setting. To search the high‐dimensional model space, where both the number of predictors and the number of possibly correlated responses can be larger than the sample size, we demonstrate that a marginalization‐based collapsed Gibbs sampler, in combination with spike and slab type of priors, offers a computationally feasible and efficient solution. As an example, we apply our method to an expression quantitative trait loci (eQTL) analysis on publicly available single nucleotide polymorphism (SNP) and gene expression data for humans where the primary interest lies in finding the significant associations between the sets of SNPs and possibly correlated genetic transcripts. Our method also allows for inference on the sparse interaction network of the transcripts (response variables) after accounting for the effect of the SNPs (predictor variables). We exploit properties of Gaussian graphical models to make statements concerning conditional independence of the responses. Our method compares favorably to existing Bayesian approaches developed for this purpose.
ISSN:0006-341X
1541-0420
DOI:10.1111/biom.12021