Spatial variational Bayesian analysis of functional magnetic resonance imaging data with spatially varying autoregressive orders

Common methods for spatio-temporal modeling of functional magnetic resonance imaging (fMRI) data often rely on low-order, constant autoregressive coefficients and simplify Bayesian approaches by neglecting spatial correlations between voxels to minimize computational demands. In contrast, this study enhances modeling by incorporating voxel correlations and addressing the heterogeneity of autoregressive error orders. This is achieved through the application of a spike and slab prior to the autoregressive coefficients, with autoregressive orders clustered using the Ising model. Parameter estimation involves estimating the Ising model parameters using the Swendsen-Wang algorithm and updating other model parameters using the Spatial Variational Bayes method, which incorporates voxel correlations and computes the posterior distribution via Gaussian Markov Random Field sampling and the preconditioned conjugate gradient method. The model’s performance, evaluated with both simulated and real data, demonstrates that accounting for autoregressive order heterogeneity and voxel correlations leads to more accurate results.