# A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis

## TL;DR

This paper introduces a Bayesian general linear model for cortical surface fMRI data analysis, offering improved spatial modeling, activation detection, and multi-subject analysis over classical methods.

## Contribution

It presents the first Bayesian spatial model for cs-fMRI, utilizing INLA for efficient computation and an excursions set method for activation detection without multiple comparisons correction.

## Key findings

- Smoother activation estimates with the Bayesian model.
- More accurate false positive control.
- Higher power to detect true activations.

## Abstract

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in Bayesian spatial models. However, as no Bayesian spatial model has been proposed for cs-fMRI data, most analyses continue to employ the classical, voxel-wise general linear model (GLM) (Worsley and Friston 1995). Here, we propose a Bayesian GLM for cs-fMRI, which employs a class of sophisticated spatial processes to flexibly model latent activation fields. We use integrated nested Laplacian approximation (INLA), a highly accurate and efficient Bayesian computation technique (Rue et al. 2009). To identify regions of activation, we propose an excursions set method based on the joint posterior distribution of the latent fields, which eliminates the need for multiple comparisons correction. Finally, we address a gap in the existing literature by proposing a novel Bayesian approach for multi-subject analysis. The methods are validated and compared to the classical GLM through simulation studies and a motor task fMRI study from the Human Connectome Project. The proposed Bayesian approach results in smoother activation estimates, more accurate false positive control, and increased power to detect truly active regions.