Illustration and definition of quantities used in the analysis. A UHECR with a known rigidity r, enters the Galaxy with an arrival direction θ_true (red dot). Because of the GMF, it is deflected and is observed on Earth as arriving from θ_obs (black dot). The angular distance between θ_obs and θ_true is α, and it is the error that the GMF induces on the observed arrival direction. We traced back the particle through each GMF configuration sampled using NIFTy, thus ending up with a distribution of arrival directions P(θ|D), with D defined in Eq. (16). From the posterior samples drawn, we calculated the mean angular distances ⟨δθ⟩_θ|D and ⟨δϕ⟩_θ|D to the true and observed arrival directions, respectively, as well as the standard deviations for the former. The scales in this artificial example are larger for visual clarity, and do not correspond to an application of the method.