Bayesian spatiotemporal modeling on complex‐valued fMRI signals via kernel convolutions

We propose a model‐based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex‐valued functional magnetic resonance imaging (CV‐fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel‐based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex‐valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task‐related CV‐fMRI data. In addition, we show that complex‐valued approaches dominate magnitude‐only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level.