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June 2015 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, James A. Coan
Ann. Appl. Stat. 9(2): 687-713 (June 2015). DOI: 10.1214/15-AOAS818

Abstract

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.

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Fan Li. Tingting Zhang. Quanli Wang. Marlen Z. Gonzalez. Erin L. Maresh. James A. Coan. "Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression." Ann. Appl. Stat. 9 (2) 687 - 713, June 2015. https://doi.org/10.1214/15-AOAS818

Information

Received: 1 October 2014; Revised: 1 February 2015; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499926
MathSciNet: MR3371331
Digital Object Identifier: 10.1214/15-AOAS818

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.9 • No. 2 • June 2015
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