  Observations by the Interface Region Imaging Spectrograph (IRIS) in the Mg II
h & k spectral lines have provided a new diagnostic window towards the
knowledge of the complex physical conditions in the solar chromosphere.
Theoretical efforts focused on understanding the behavior of these lines have
allowed us to obtain a better and more accurate vision of the chromosphere.
These efforts include forward modeling, numerical simulations, and inversions.
In this paper, we focus our attention on the uncertainties associated with the
thermodynamic model atmosphere obtained after the inversion of the Mg II h & k
lines. We have used ~ 50;000 synthetic representative profiles of the IRIS2
database to characterize the most important source of uncertainties in the
inversion process, viz.: the inherent noise of the observations, the random
initialization of process, and the selection criteria in a high-dimensional
space. We have applied a Monte Carlo approach to this problem. Thus, for a
given synthetic representative profile, we have created five randomized noise
realizations (representative of the most popular exposure times in the IRIS
observations), and inverted these profiles five times with different inversion
initializations. The resulting 25 inverted profiles, fits to noisy data, and
model atmospheres are then used to determine the uncertainty in the model
atmosphere, based on the standard deviation and empirical selection criteria
for the goodness of fit. With this approach, the new uncertainties of the
models available in the IRIS2 database are more reliable at the optical depths
where the Mg II h & k lines are sensitive to changes in the thermodynamics.
