Statistics Papers

Document Type

Journal Article

Date of this Version

2010

Publication Source

Journal of the American Statistical Association

Volume

105

Issue

491

Start Page

1202

Last Page

1214

DOI

10.1198/jasa.2010.tm08177

Abstract

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.

Copyright/Permission Statement

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.

Comments

At the time of publication, author Nancy R. Zhang was affiliated with Stanford University. Currently, she is a faculty member at the Statistics Department at the University of Pennsylvania.

Keywords

Ising model, Markov chain Monte Carlo, motif analysis, phase transition, undirected graph

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Date Posted: 27 November 2017