  The central aim in this paper is to address variable selection questions in
nonlinear and nonparametric regression. Motivated by statistical genetics,
where nonlinear interactions are of particular interest, we introduce a novel
and interpretable way to summarize the relative importance of predictor
variables. Methodologically, we develop the "RelATive cEntrality" (RATE)
measure to prioritize candidate genetic variants that are not just marginally
important, but whose associations also stem from significant covarying
relationships with other variants in the data. We illustrate RATE through
Bayesian Gaussian process regression, but the methodological innovations apply
to other "black box" methods. It is known that nonlinear models often exhibit
greater predictive accuracy than linear models, particularly for phenotypes
generated by complex genetic architectures. With detailed simulations and two
real data association mapping studies, we show that applying RATE enables an
explanation for this improved performance.
