  Inferring magnetic and thermodynamic information from spectropolarimetric
observations relies on the assumption of a parameterized model atmosphere whose
parameters are tuned by comparison with observations. Often, the choice of the
underlying atmospheric model is based on subjective reasons. In other cases,
complex models are chosen based on objective reasons (for instance, the
necessity to explain asymmetries in the Stokes profiles) but it is not clear
what degree of complexity is needed. The lack of an objective way of comparing
models has, sometimes, led to opposing views of the solar magnetism because the
inferred physical scenarios are essentially different. We present the first
quantitative model comparison based on the computation of the Bayesian evidence
ratios for spectropolarimetric observations. Our results show that there is not
a single model appropriate for all profiles simultaneously. Data with moderate
signal-to-noise ratios favor models without gradients along the line-of-sight.
If the observations shows clear circular and linear polarization signals above
the noise level, models with gradients along the line are preferred. As a
general rule, observations with large signal-to-noise ratios favor more complex
models. We demonstrate that the evidence ratios correlate well with simple
proxies. Therefore, we propose to calculate these proxies when carrying out
standard least-squares inversions to allow for model comparison in the future.
