Models of the diffusion-weighted signal are of strong interest for population studies of the brain microstructure. These studies are typically conducted by extracting a scalar property from the model and subjecting it to null hypothesis significance testing. This process has two major limitations: the reported p-value is a weak predictor of the reproducibility of findings and evidence for the absence of microstructural alterations cannot be gained. To overcome these limitations, this paper proposes a Bayesian framework for population studies of the brain microstructure represented by multi-fascicle models. A hierarchical model is built over the biophysical parameters of the microstructure. Bayesian inference is performed by Hamiltonian Monte Carlo sampling and results in a joint posterior distribution over the latent microstructure parameters for each group. Inference from this posterior enables richer analyses of the brain microstructure beyond the dichotomy of significance testing. Using synthetic and in-vivo data, we show that our Bayesian approach increases reproducibility of findings from population studies and opens new opportunities in the analysis of the brain microstructure.