Hierarchical mixed effects models have been demonstrated to be particularly powerful for predicting genomic merit of livestock and plants based on high density single nucleotide polymorphism (SNP) marker panels, and their use is being increasingly advocated for genomic predictions in human health. Two particularly popular approaches, labeled BayesA and BayesB, are based on specifying all SNP-associated effects to be independent of each other. BayesB extends BayesA by allowing a large proportion of SNP markers to be associated with null effects. We further extend these two models to specify SNP effects as being spatially correlated due to the chromosomally proximal effects of causal variants. These two models, that we respectively dub as ante-BayesA and ante-BayesB, are based on a first order nonstationary antedependence specification between SNP effects. In a simulation study involving 20 replicate datasets, each analyzed at six different SNP marker densities with average LD levels ranging from r2=0.15 to 0.31, the antedependence methods had significantly (P <0.01) higher accuracies than their corresponding classical counterparts at higher LD levels (r2 > 0. 24) with differences exceeding 3%. A cross-validation study was also conducted on the heterogeneous stock mice data resource (http://mus.well.ox.ac.uk/mouse/HS/) using 6 week body weights as the phenotype. The antedependence-based methods increased cross-validation prediction accuracies by up to 3.6% compared to their classical counterparts (P < 0.001).