  It is shown that the two-part Minimum Description Length Principle can be
used to discriminate among different models that can explain a given observed
dataset. The description length is chosen to be the sum of the lengths of the
message needed to encode the model plus the message needed to encode the data
when the model is applied to the dataset. It is verified that the proposed
principle can efficiently distinguish the model that correctly fits the
observations while avoiding over-fitting. The capabilities of this criterion
are shown in two simple problems for the analysis of observed
spectropolarimetric signals. The first is the de-noising of observations with
the aid of the PCA technique. The second is the selection of the optimal number
of parameters in LTE inversions. We propose this criterion as a quantitative
approach for distinguising the most plausible model among a set of proposed
models. This quantity is very easy to implement as an additional output on the
existing inversion codes.
