Genome-wide association studies (GWAS) have largely failed to identify most of the genetic basis of highly heritable diseases and complex traits. Recent work has suggested this could be because many genetic variants, each with individually small effects, compose their genetic architecture, limiting the power of GWAS, given currently obtainable sample sizes. In this scenario, Bonferroni-derived thresholds are severely underpowered to detect the vast majority of associations. Local false discovery rate (fdr) methods provide more power to detect non-null associations, but implicit assumptions about the exchangeability of single nucleotide polymorphisms (SNPs) limit their ability to discover non-null loci.