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Title: Graph-structured variable selection with Gaussian Markov random field horseshoe prior Authors:  Marie Denis - CIRAD, Georgetown University (France) [presenting]
Mahlet Tadesse - Georgetown University (United States)
Abstract: A graph structure is commonly used to characterize the dependence between variables. The Bayesian approach provides a natural framework to integrate the graph information through the prior distributions. We present an approach that combines Gaussian Markov random field (MRF) prior with global-local (GL) shrinkage prior for the selection of graph-structured variables. The local shrinkage parameters capture the dependence between connected covariates and take into account the sign of their empirical correlations. This encourages a similar amount of shrinkage for the regression coefficients while allowing them to have opposite signs. For non-connected variables, a standard horseshoe prior is specified. We illustrate the performance of the model with simulated data and real data applications, one in quantitative trait loci mapping with dependence between adjacent genetic markers and the other in gene expression data with a general estimated dependence structure between genes.