Population structure due to phylogenetic relationships between
subjects can cause inaccurate predictions in association studies. The
confounding effects of this structure have been revisited in multiple
biological disciplines resulting in a disparate collection of proposed
solutions. With few exceptions, these solutions fall short in one of
two ways: they seek only to calibrate p-values (e.g., Genomic
Control); or they assume a flat population structure (e.g., Structured
Association, PCA). I will discuss statistical models, known as
generative or graphical models that explicitly address both these
issues. I'll show that these models identify associations with fewer
false positives and false negatives than existing methods, and provide
a method that accurately estimates the false positive rate of
associations identified by the models. I'll demonstrate the utility of
these models in several domains including HLA-mediated immune pressure
on HIV evolution, networks of compensatory mutations in an HIV
protein, and a genome wide association (GWA) study in which standard
population structure-correcting methods are known to fail.