Exact and analytic bayesian inference for orientation distribution functions

Characterizing the fibre orientation uncertainty is essential for quantitative tractography approaches, such as probabilistic tracking. We present an analytic way to perform Bayesian inference on diffusion ODFs from Q-ball imaging data. Drawing a random sample of ODFs reduces to sampling a multivariate t distribution. Assuming that the local ODF maxima provide fibre orientations, a random sample of orientations can then be directly obtained from the ODF sample. Contrary to approximate inference approaches, such as MCMC, our method samples from the exact posterior distribution. Results are illustrated on simulated and human in-vivo data.