  The reconstruction of the differential emission measure (DEM) from
observations of spectral line intensities provides information on the
temperature distribution of the emission measure in the region observed. The
inversion process is known to be highly unstable and it has been necessary to
provide additional constraints, such as requiring that the DEM should be
smooth. However, this is a non-physical constraint. The goal of this analysis
is to make an empirical determination of the ability of a set of emission line
intensities to constrain the reconstruction. Here, a simple model is used, by
means of a Monte-Carlo-Markov-Chain process, to arrive at solutions that
reproduces the observed intensities in a region of the quiet Sun and a solar
active region. These solutions are compared by means of the reduced
chi-squared. The conclusion from this analysis is that the observations are
only capable of constraining model consisting of 4 temperature-emission measure
pairs plus a determination of the standard deviation of the model from the
observed line intensities. A more complex model with 5 temperature-emission
measure pairs does not improve the fit and leads to parameters that are
irrelevant. A more general conclusion is that the information content of a set
of observed emission lines is limited with respect to the determination of the
emission measure distribution.
