  Identifying genetic variants that regulate quantitative traits, or QTLs, is
the primary focus of the field of statistical genetics. Most current methods
are limited to identifying mean effects, or associations between genotype and
the mean value of a quantitative trait. It is possible, however, that a genetic
variant may affect the variance of the quantitative trait in lieu of, or in
addition to, affecting the trait mean. Here, we develop a general
methodological approach to identifying covariates with variance effects on a
quantitative trait using a Bayesian heteroskedastic linear regression model. We
show that our Bayesian test for heteroskedasticity (BTH) outperforms classical
tests for differences in variation across a large range of simulations drawn
from scenarios common to the analysis of quantitative traits. We apply BTH to
methylation QTL study data and expression QTL study data to identify variance
QTLs. When compared with three tests for heteroskedasticity used in genomics,
we illustrate the benefits of using our approach, including avoiding
overfitting by incorporating uncertainty and flexibly identifying
heteroskedastic effects.
