Functional MRI (fMRI) is a recent, non-invasive technique allowing for the evolution of brain processes to be dynamically followed in various cognitive or behavioral tasks. In BOLD fMRI, what is actually measured is only indirectly related to neuronal activity through a process that is still under investigation. A convenient way to analyze BOLD fMRI data consists of considering the whole brain as a system characterized by a transfer response function, called the Hemodynamic Response Function (HRF). Precise and robust estimation of the HRF has not been achieved yet: parametric methods tend to be robust but require too strong constraints on the shape of the HRF, whereas non-parametric models are not reliable since the problem is badly conditioned. We therefore propose a full Bayesian, non-parametric method that makes use of basic but relevant a priori knowledge about the underlying physiological process to make robust inference about the HRF. We show that this model is very robust to decreasing signal-to-no...