Date of this Version
Journal of the American Statistical Association
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.
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 01 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/jasa.2010.tm08177.
Ising model, Markov chain Monte Carlo, motif analysis, phase transition, undirected graph
Li, F., & Zhang, N. R. (2010). Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces With Applications in Genomics. Journal of the American Statistical Association, 105 (491), 1202-1214. http://dx.doi.org/10.1198/jasa.2010.tm08177
Date Posted: 27 November 2017