  We introduce a sparse high-dimensional regression approach that can
incorporate prior information on the regression parameters and can borrow
information across a set of similar datasets. Prior information may for
instance come from previous studies or genomic databases, and information
borrowed across a set of genes or genomic networks. The approach is based on
prior modelling of the regression parameters using the horseshoe prior, with a
prior on the sparsity index that depends on external information. Multiple
datasets are integrated by applying an empirical Bayes strategy on
hyperparameters. For computational efficiency we approximate the posterior
distribution using a variational Bayes method. The proposed framework is useful
for analysing large-scale data sets with complex dependence structures. We
illustrate this by applications to the reconstruction of gene regulatory
networks and to eQTL mapping.
