Selection of temporal models for event related fMRI

In functional magnetic resonance imaging (fMRI), recent works have addressed the non parametric estimation of the hemodynamic response function (HRF) under linearity and stationarity in time hypotheses. We propose to test a more flexible model that allows for the variation of the magnitude of the HRF with time. Under this model, the magnitude of the HRF evoked by a single event may vary with other occurrences of the same kind of event. This model is tested against a simpler model with a fixed magnitude. We develop a stochastic version of the EM algorithm to identify the magnitudes and the HRF. We also address the problem of model specification. It is usually assumed that every event type evokes a response. Our scheme uses a model selection approach which provides the best subset of event types maximizing the likelihood of the fMRI signal. Our methodology is exemplified by simulated and fMRI data.