Functional Magnetic Resonance Imaging (fMRI) is an exciting and rapidly developing tool that enables cognitive psychologists and neuroscientists to study the human brain in action. During an fMRI experiment, subjects perform a set of cognitive tasks while images of their brain are acquired. Psychologists use these data to build and test models of human cognitive processing.

Most current statistical methods for the analysis of fMRI data are based on the classification of ``active" locations in the brain. While identifying the location of neural activity is an important first step, a more sophisticated approach is needed to address many of the scientific questions to which fMRI data is applied. Moreover, many of the classification methods---based on hypothesis tests---are founded on simplistic statistical models, and few of these can evolve as new information about the underlying processes comes to light.

I will describe a family of statistical models for fMRI data that can account for some of the complexity in fMRI data. I will also present a framework for inference that enables investigators to address a much broader range of scientific questions, to test the predictions of cognitive theories, and to integrate fMRI results with other sources of information. This work offers several lessons---both computational and conceptual---for dealing with data realized from general spatio-temporal processes. Using examples from fMRI experiments, I illustrate the approach and demonstrate its advantages.

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