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Fully Bayesian Spatio-temporal Modelling of FMRI Data

FMRIB Technical Report TR03MW2
(A related paper has been accepted for publication in IEEE TMI)

Mark W. Woolrich, Mark Jenkinson, J. Michael Brady and Stephen M. Smith

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK
Corresponding author is Mark Woolrich:


We present a fully Bayesian approach to modelling in FMRI, incorporating spatio-temporal noise modelling and haemodynamic response function (HRF) modelling. A fully Bayesian approach allows for the uncertainties in the noise and signal modelling to be incorporated together to provide full posterior distributions of the HRF parameters. The noise modelling is achieved via a non-separable space-time vector autoregressive process. Previous FMRI noise models have either been purely temporal, separable or modelling deterministic trends. The specific form of the noise process is determined using model selection techniques. Notably, this results in the need for a spatially non-stationary and temporally stationary spatial component. Within the same full model, we also investigate the variation of the HRF in different areas of the activation, and for different experimental stimuli. We propose a novel HRF model made up of half-cosines, which allows distinct combinations of parameters to represent characteristics of interest. In addition, to adaptively avoid over-fitting we propose the use of Automatic Relevance Determination priors to force certain parameters in the model to zero with high precision if there is no evidence to support them in the data. We apply the model to three datasets and observe matter-type dependence of the spatial and temporal noise, and a negative correlation between activation height and HRF time to main peak (although we suggest that this apparent correlation may be due to a number of different effects).

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Next: Introduction