Dissecting galaxy formation models with Sensitivity Analysis -- A new
  approach to constrain the Milky Way formation history
  [Abridged] We present an application of a statistical tool known as
Sensitivity Analysis to characterize the relationship between input parameters
and observational predictions of semi-analytic models of galaxy formation
coupled to cosmological $N$-body simulations. We show how a sensitivity
analysis can be performed on our chemo-dynamical model, ChemTreeN, to
characterize and quantify its relationship between model input parameters and
predicted observable properties. The result of this analysis provides the user
with information about which parameters are most important and most likely to
affect the prediction of a given observable. It can also be used to simplify
models by identifying input parameters that have no effect on the outputs of
interest. Conversely, it allows us to identify what model parameters can be
most efficiently constrained by the given observational data set. We have
applied this technique to real observational data sets associated with the
Milky Way, such as the luminosity function of satellite galaxies. A statistical
comparison of model outputs and real observables is used to obtain a
"best-fitting" parameter set. We consider different Milky Way-like dark matter
halos to account for the dependence of the best-fitting parameters selection
process on the underlying merger history of the models. For all formation
histories considered, running ChemTreeN with best-fitting parameters produced
luminosity functions that tightly fit their observed counterpart. However, only
one of the resulting stellar halo models was able to reproduce the observed
stellar halo mass within 40 kpc of the Galactic center. On the basis of this
analysis it is possible to disregard certain models, and their corresponding
merger histories, as good representations of the underlying merger history of
the Milky Way.
