Bayesian inference for group-level cortical surface image-on-scalar regression with Gaussian process priors.

In regression-based analyses of group-level neuroimage data, researchers typically fit a series of marginal general linear models to image outcomes at each spatially referenced pixel. Spatial regularization of effects of interest is usually induced indirectly by applying spatial smoothing to the data during preprocessing. While this procedure often works well, the resulting inference can be poorly calibrated. Spatial modeling of effects of interest leads to more powerful analyses; however, the number of locations in a typical neuroimage can preclude standard computing methods in this setting. Here, we contribute a Bayesian spatial regression model for group-level neuroimaging analyses. We induce regularization of spatially varying regression coefficient functions through Gaussian process priors. When combined with a simple non-stationary model for the error process, our prior hierarchy can lead to more data-adaptive smoothing than standard methods. We achieve computational tractability through a Vecchia-type approximation of our prior that retains full spatial rank and can be constructed for a wide class of spatial correlation functions. We outline several ways to work with our model in practice and compare performance against standard vertex-wise analyses and several alternatives. Finally, we illustrate our methods in an analysis of cortical surface functional magnetic resonance imaging task contrast data from a large cohort of children enrolled in the adolescent brain cognitive development study.