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Abstract:
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In many fields, a graph structure is used to characterize the dependence among variables. This dependence may be induced by time, space, biological networks, or other factors. Incorporating this dependence structure can improve the performance of variable selection. The Bayesian approach provides a natural framework to integrate the graph information using appropriate priors that may be placed on the variable selection indicators or directly on the regression coefficients. In this work we propose combining a Gaussian Markov random field (MRF) prior with a global–local (GL) shrinkage prior to select graph-structured variables. The local shrinkage parameters provide flexibility in the amount of shrinkage and smoothness of the coefficients for the connected variables, while the global parameter performs shrinkage on all coefficients. We also integrate the sign of correlations among connected variables to allow their regression coefficients to take opposite signs. We illustrate the different models with simulated data and an application examining the impact of gene expression levels on riboflavin production by Bacillus subtilis.
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