We readdress the diffusion tractography problem in a global and probabilistic manner. Instead of tracking through local orientations, we parameterise the connexions between brain regions at a global level, and then infer on global and local parameters simultaneously in a Bayesian framework. This approach offers a number of important benefits. The global nature of the tractography reduces sensitivity to local noise and modelling errors. By constraining tractography to ensure a connexion is found, and then inferring on the exact location of the connexion, we increase the robustness of connectivity-based parcellations, allowing parcellations of connexions that were previously invisible to tractography. The Bayesian framework allows a direct comparison of the evidence for connecting and non-connecting models, to test whether the connexion is supported by the data. Crucially, by explicit parameterisation of the connexion between brain regions, we infer on a parameter that is shared with models of functional connectivity. This model is a first step toward the joint inference on functional and anatomical connectivity.