  Genome-wide association studies have proven to be essential for understanding
the genetic basis of disease. However, many complex traits---personality
traits, facial features, disease subtyping---are inherently high-dimensional,
impeding simple approaches to association mapping. We developed a nonparametric
Bayesian reduced rank regression model for multi-SNP, multi-trait association
mapping that does not require the rank of the linear subspace to be specified.
We show in simulations and real data that our model shares strength over SNPs
and over correlated traits, improving statistical power to identify genetic
associations with an interpretable, SNP-supervised low-dimensional linear
projection of the high-dimensional phenotype. On the HapMap phase 3 gene
expression QTL study data, we identify pleiotropic expression QTLs that
classical univariate tests are underpowered to find and that two step
approaches cannot recover. Our Python software, BERRRI, is publicly available
at GitHub: https://github.com/ashlee1031/BERRRI.
