Abstract

A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically sig-

nificant. In this article, we propose a Bayesian nonparametric spatially varying correlation model to make

inference of such regions. We build our model based on the thresholded correlation Gaussian process

(TCGP). It ensures piecewise smoothness, sparsity, and jump discontinuity of spatially varying correlations, and is well applicable even when the number of subjects is limited or the signal-to-noise ratio is low.

We study the identifiability of our model, establish the large support property, and derive the posterior

consistency and selection consistency. We also develop a highly efficient Gibbs sampler and its variant

to compute the posterior distribution. We illustrate the method with both simulations and an analysis of

functional magnetic resonance imaging data from the Human Connectome Project.

Information

Preprint No.SS-2023-0312
Manuscript IDSS-2023-0312
Complete AuthorsMoyan Li, Lexin Li, Jian Kang
Corresponding AuthorsJian Kang
Emailsjiankang@umich.edu

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Acknowledgments

This work was supported by NIH grants R01DA048993, R01MH105561, R01GM124061,

and NSF grant IIS2123777. We thank the associate editor and anonymous reviewers for

their constructive comments and insightful suggestions, which significantly improved the

quality and clarity of the manuscript.

Supplementary Materials

In the Supplement Material, we first present the proofs of all the theoretical results in the paper, along with a number of useful lemmas. We next derive the full conditional distributions

of the model parameters, and present some additional numerical results.

Supplementary materials are available for download.