A. Aubert and R. Costalat, A Model of the Coupling between Brain Electrical Activity, Metabolism, and Hemodynamics: Application to the Interpretation of Functional Neuroimaging, NeuroImage, vol.17, issue.3, pp.1162-1181, 2002.
DOI : 10.1006/nimg.2002.1224

R. M. Birn, Z. S. Saad, and P. A. Bandettini, Spatial Heterogeneity of the Nonlinear Dynamics in the FMRI BOLD Response, NeuroImage, vol.14, issue.4, pp.817-826, 2001.
DOI : 10.1006/nimg.2001.0873

G. E. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, 1992.
DOI : 10.1002/9781118033197

G. M. Boynton, S. A. Engel, G. H. Glover, and D. J. Heeger, Linear systems analysis of functional magnetic resonance imaging in human v1, The Journal of Neuroscience, vol.16, pp.4207-4221, 1996.

R. B. Buxton and L. R. Frank, A Model for the Coupling Between Cerebral Blood Flow and Oxygen Metabolism During Neural Stimulation, Journal of Cerebral Blood Flow & Metabolism, vol.10, issue.5, pp.64-72, 1997.
DOI : 10.1097/00004647-199701000-00009

R. B. Buxton, K. Uluda?, D. J. Dubowitz, and T. T. Liu, Modeling the hemodynamic response to brain activation, NeuroImage, vol.23, pp.220-233, 2004.
DOI : 10.1016/j.neuroimage.2004.07.013

R. B. Buxton, E. C. Wang, and L. R. Frank, Dynamics of blood flow and oxygenation changes during brain activation: The balloon model, Magnetic Resonance in Medicine, vol.77, issue.6, pp.855-864, 1998.
DOI : 10.1002/mrm.1910390602

M. Dale and A. , Selective averaging of rapidly presented individual trials using fmri, pp.329-390, 1997.

T. L. Davis, K. K. Kwong, R. M. Weisskoff, and B. R. Rosen, Calibrated functional MRI: Mapping the dynamics of oxidative metabolism, Proceedings of the National Academy of Sciences, vol.48, issue.1-2, pp.1834-1839, 1998.
DOI : 10.1073/pnas.87.16.6082

K. Friston, O. Josephs, G. Rees, T. , and R. , Nonlinear event-related responses in fMRI, Magnetic Resonance in Medicine, vol.4, issue.1, pp.41-52, 1998.
DOI : 10.1002/mrm.1910390109

K. J. Friston, Bayesian Estimation of Dynamical Systems: An Application to fMRI, NeuroImage, vol.16, issue.2, pp.513-530, 2002.
DOI : 10.1006/nimg.2001.1044

K. J. Friston, A. P. Holmes, K. J. Worsley, J. Poline, C. D. Frith et al., Statistical parametric maps in functional imaging: A general linear approach, Human Brain Mapping, vol.26, issue.4, pp.189-210, 1995.
DOI : 10.1002/hbm.460020402

K. J. Friston, A. Mechelli, R. Turner, P. , and C. J. , Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics, NeuroImage, vol.12, issue.4, pp.466-477, 2000.
DOI : 10.1006/nimg.2000.0630

K. J. Friston and K. J. Worsley, Analysis of fMRI Time-Series Revisited, NeuroImage, vol.2, issue.1, pp.45-53, 1995.
DOI : 10.1006/nimg.1995.1007

A. Gelman, J. B. Carlin, H. S. Stern, R. , and D. B. , Bayesian Data Analysis, 1998.

G. H. Glover, Deconvolution of impulse response in event-related bold fmri, pp.416-445, 1999.

R. D. Hoge, M. A. Franceschini, R. J. Covolan, T. Huppert, J. B. Mandeville et al., Simultaneous recording of task-induced changes in blood oxygenation, volume, and flow using diffuse optical imaging and arterial spin-labeling MRI, NeuroImage, vol.25, issue.3, pp.701-707, 2005.
DOI : 10.1016/j.neuroimage.2004.12.032

C. Janz, S. P. Heinrich, J. Kornmayer, M. Bach, and J. Hennig, Coupling of neural activity and BOLD fMRI response: New insights by combination of fMRI and VEP experiments in transition from single events to continuous stimulation, Magnetic Resonance in Medicine, vol.71, issue.3, pp.482-488, 2001.
DOI : 10.1002/mrm.1217

J. Kershaw, B. A. Ardekani, and I. Kanno, Application of Bayesian inference to fMRI data analysis, IEEE Transactions on Medical Imaging, vol.18, issue.12, pp.1138-1153, 1999.
DOI : 10.1109/42.819324

G. Krüger, A. Kastrup, A. Takahashi, and G. H. Glover, Simultaneous monitoring of dynamic changes in cerebral blood flow and oxygenation during sustained activation of the human visual cortex, NeuroReport, vol.10, issue.14, pp.2939-2943, 1999.
DOI : 10.1097/00001756-199909290-00012

N. K. Logothetis and J. Pfeuffer, On the nature of the BOLD fMRI contrast mechanism, Magnetic Resonance Imaging, vol.22, issue.10, pp.1517-1548, 2004.
DOI : 10.1016/j.mri.2004.10.018

D. W. Marquardt, An Algorithm for Least-Squares Estimation of Nonlinear Parameters, Journal of the Society for Industrial and Applied Mathematics, vol.11, issue.2, pp.431-441, 1963.
DOI : 10.1137/0111030

K. L. Miller, W. Luh, T. T. Liu, A. Martinez, T. Obata et al., Nonlinear temporal dynamics of the cerebral blood flow response, Human Brain Mapping, vol.6, issue.1, pp.1-12, 2001.
DOI : 10.1002/hbm.1020

T. Obata, T. T. Liu, K. L. Miller, W. M. Luh, E. C. Wong et al., Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the balloon model to the interpretation of BOLD transients, NeuroImage, vol.21, issue.1, pp.144-153, 2004.
DOI : 10.1016/j.neuroimage.2003.08.040

S. Ogawa, R. S. Menon, D. W. Tank, S. Kim, H. Merkle et al., Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model, Biophysical Journal, vol.64, issue.3, pp.803-812, 1993.
DOI : 10.1016/S0006-3495(93)81441-3

J. Riera, E. Aubert, K. Iwata, R. Kawashima, X. Wan et al., Fusing EEG and fMRI based on a bottom-up model: inferring activation and effective connectivity in neural masses, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.21, issue.4, pp.1025-1041, 2005.
DOI : 10.1002/hbm.20000

J. Riera, J. Watanabe, I. Kazuki, M. Naoki, E. Aubert et al., A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals, NeuroImage, vol.21, issue.2, pp.547-567, 2004.
DOI : 10.1016/j.neuroimage.2003.09.052

A. L. Vazquez and D. C. Noll, Nonlinear Aspects of the BOLD Response in Functional MRI, NeuroImage, vol.7, issue.2, pp.108-118, 1998.
DOI : 10.1006/nimg.1997.0316

T. D. Wager, A. Vazquez, L. Hernandez, and D. C. Noll, Accounting for nonlinear BOLD effects in fMRI: parameter estimates and a model for prediction in rapid event-related studies, NeuroImage, vol.25, issue.1, pp.206-224, 2005.
DOI : 10.1016/j.neuroimage.2004.11.008

Y. Zheng, J. Martindale, D. Johnson, M. Jones, J. Berwick et al., A Model of the Hemodynamic Response and Oxygen Delivery to Brain, NeuroImage, vol.16, issue.3, pp.617-637, 2002.
DOI : 10.1006/nimg.2002.1078

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