Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and effective SNPs makes the use of sparse modeling of such genetic data sets, highly important. The high-dimensional sparse instrumental variables models are one of such useful association models, which models the simultaneous relation of the gene expressions and genetic variants with complex traits. From a Bayesian viewpoint, the sparsity can be favored using sparsity-enforcing priors such as spike-and-slab priors. A two-stage modification of the expectation propagation (EP) algorithm is proposed and examined for approximate inference in high-dimensional sparse instrumental variables models with spike-and-slab priors. This method is an adoption of the classical two-stage least squares method, to be used with the Bayes context. A simulation study is performed to examine the performance of the methods. The proposed method is applied to analysis of the mouse obesity data.
