Bayesian variable selection in structured high-dimensional covariate spaces with applications in genomics. (English) Zbl 1390.62027
Summary: We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the model building process. We approach this problem through the Bayesian variable selection framework, where we assume that the covariates lie on an undirected graph and formulate an Ising prior on the model space for incorporating structural information. Certain computational and statistical problems arise that are unique to such high-dimensional, structured settings, the most interesting being the phenomenon of phase transitions. We propose theoretical and computational schemes to mitigate these problems. We illustrate our
methods on two different graph structures: the linear chain and the regular graph of degree \(k\). Finally, we use our methods to study a specific application in genomics: the modeling of transcription factor binding sites in DNA sequences.
MSC:
62F07 | Statistical ranking and selection procedures |
62F15 | Bayesian inference |
62J05 | Linear regression; mixed models |
62P10 | Applications of statistics to biology and medical sciences; meta analysis |