Functional Magnetic Resonance Imaging (fMRI) is a new technique for studying the workings of the active human brain. During an fMRI experiment, a sequence of Magnetic Resonanc images is acquired while a subject performs specific behavioral tasks. Changes in the measured signal can be used to identify and characterize the brain activity resulting from task performance and thus help to understand how higher cognition emerges from the brain's architecture.
The data obtained from an fMRI experiment are a realization of a complex spatio-temporal process with many sources of variation, both biological and technological. The noise is complicated, and the task-related signal changes are small in amplitude. Here, we describe a new and detailed statistical model for fMRI data and present inferential methods that enable investigators to directly target their scientific questions of interest, many of which are inaccessible to current methods. Our model allows for the complexity of the noise process, flexibly parameterizes the task-related signal changes, and allows for non-linearity and non-additivity in the system response.