The first and second columns show the marginal posterior for the hyperparameters of the von-Mises prior for the misalignment (upper panels) and the log-normal prior for the perpendicular component of the magnetic field (lower panels) for the case of the penumbra. The plots show a histogram and a kernel density estimation using the samples. The rightmost column shows the Montecarlo estimate of the prior distribution for all considered pixels for both parameters.