Genomic best linear unbiased prediction (GBLUP) analyses have been increasingly adapted for genome-wide association (GWA) analyses. A currently popular modification of GBLUP for GWA, which we label as classic GBLUP, is to treat all genetic markers as random, except for the marker being tested; conversely, shrinkage GBLUP treats all markers as random in a whole genome prediction (WGP) analysis. The classic GBLUP modification has been demonstrated to preserve Type I error rates whereas shrinkage GBLUP leads to a very conservative GWA test. Nevertheless, shrinkage estimation has recently been shown to have GWA properties under alternative prior specifications. Some popular WGP model specifications are heavy-tailed (i.e., BayesA) or involve variable selection (i.e., BayesSSVS) that do not shrink large marker effects as much as shrinkage GBLUP. Given that MCMC implementations of these models are computationally onerous, we propose inferences under these alternative priors based on the EM algorithm (i.e., EMBayesA and EMBayesSSVS). In a simulation involving 10 replicated data sets, each involving about 2000 individuals and 5000 SNP markers with average pairwise LD r² = 0.30 across 5 chromosomes, we discovered that EMBayesA and EMBayesSSVS shrink the majority of the posterior z-score based P-values to be larger relative to classic GBLUP, whereas markers in QTL regions tend to have substantially smaller P-values in EMBayesA and EMBayesSSVS compared with classic GBLUP. In an application involving backfat data from a Duroc-Pietrain F2 cross, we determined that EMBayesSSVS inferred SNP effects in albeit fewer putative QTL regions compared with classical GBLUP, although GWA using EMBayesA did not detect any such association. We suggest that EMBayesSSVS or other hierarchical variable selection models represent promising alternatives for GWA analyses of complex traits for which null marker effects might not appropriately represent a global null hypothesis; however, we also demonstrate that recently developed regularization techniques are vitally important in helping avoid posterior multimodality concerns in large dimensional EM-based inferences as well.