The Annals of Applied Statistics

Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression

Fan Li, Tingting Zhang, Quanli Wang, Marlen Z. Gonzalez, Erin L. Maresh, and James A. Coan

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Multi-subject functional magnetic resonance imaging (fMRI) data has been increasingly used to study the population-wide relationship between human brain activity and individual biological or behavioral traits. A common method is to regress the scalar individual response on imaging predictors, known as a scalar-on-image (SI) regression. Analysis and computation of such massive and noisy data with complex spatio-temporal correlation structure is challenging. In this article, motivated by a psychological study on human affective feelings using fMRI, we propose a joint Ising and Dirichlet Process (Ising-DP) prior within the framework of Bayesian stochastic search variable selection for selecting brain voxels in high-dimensional SI regressions. The Ising component of the prior makes use of the spatial information between voxels, and the DP component groups the coefficients of the large number of voxels to a small set of values and thus greatly reduces the posterior computational burden. To address the phase transition phenomenon of the Ising prior, we propose a new analytic approach to derive bounds for the hyperparameters, illustrated on 2- and 3-dimensional lattices. The proposed method is compared with several alternative methods via simulations, and is applied to the fMRI data collected from the KLIFF hand-holding experiment.

Article information

Ann. Appl. Stat., Volume 9, Number 2 (2015), 687-713.

Received: October 2014
Revised: February 2015
First available in Project Euclid: 20 July 2015

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Bayesian Dirichlet Process fMRI Ising model phase transition scalar-on-image regression stochastic search variable selection


Li, Fan; Zhang, Tingting; Wang, Quanli; Gonzalez, Marlen Z.; Maresh, Erin L.; Coan, James A. Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression. Ann. Appl. Stat. 9 (2015), no. 2, 687--713. doi:10.1214/15-AOAS818.

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Supplemental materials

  • Heatmaps. We provide the heatmaps of the voxels with top 10% highest posterior selection probabilities obtained, resulting from Ising-DP, Ising-Gaussian and i.i.d.-Gaussian priors, respectively, in three regressions [Li et al. (2015)].