  Solar chromospheric fibrils, as observed in the core of strong chromospheric
spectral lines, extend from photospheric field concentrations suggesting that
they trace magnetic field lines. These images have been historically used as
proxies of magnetic fields for many purposes. We use a Bayesian hierarchical
model to analyze several tens of thousands of pixels in spectro-polarimetric
chromospheric images of penumbrae and chromospheric fibrils. We compare the
alignment between the field azimuth inferred from the linear polarization
signals through the transverse Zeeman effect and the direction of the fibrils
in the image. We conclude that, in the analyzed fields of view, fibrils are
often well aligned with the magnetic field azimuth. Despite this alignment, the
analysis also shows that there is a non-negligible dispersion. In penumbral
filaments, we find a dispersion with a standard deviation of ~16 degrees, while
this dispersion goes up to ~34 degrees in less magnetized regions.
