We present a non parametric Bayesian multiscale method to characterize the Hemodynamic Response HR as function of time. This is done by extending and adapting the Multigrid Priors (MGP) method proposed in (S.D.R. Amaral, S.R. Rabbani, N. Caticha, Multigrid prior for a Bayesian approach to fMRI, NeuroImage 23 (2004) 654-662; N. Caticha, S.D.R. Amaral, S.R. Rabbani, Multigrid Priors for fMRI time series analysis, AIP Conf. Proc. 735 (2004) 27-34). We choose an initial HR model and apply the MGP method to assign a posterior probability of activity for every pixel. This can be used to construct the map of activity. But it can also be used to construct the posterior averaged time series activity for different regions. This permits defining a new model which is only data-dependent. Now in turn it can be used as the model behind a new application of the MGP method to obtain another posterior probability of activity. The method converges in just a few iterations and is quite independent of the original HR model, as long as it contains some information of the activity/rest state of the patient. We apply this method of HR inference both to simulated and real data of blocks and event-related experiments. Receiver operating characteristic (ROC) curves are used to measure the number of errors with respect to a few hyperparameters. We also study the deterioration of the results for real data, under information loss. This is done by decreasing the signal to noise ratio and also by decreasing the number of images available for analysis and compare the robustness to other methods.