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[Abridged] We present an application of a statistical tool known asSensitivity Analysis to characterize the relationship between input parametersand observational predictions of semi-analytic models of galaxy formationcoupled to cosmological $N$-body simulations. We show how a sensitivityanalysis can be performed on our chemo-dynamical model, ChemTreeN, tocharacterize and quantify its relationship between model input parameters andpredicted observable properties. The result of this analysis provides the userwith information about which parameters are most important and most likely toaffect the prediction of a given observable. It can also be used to simplifymodels by identifying input parameters that have no effect on the outputs ofinterest. Conversely, it allows us to identify what model parameters can bemost efficiently constrained by the given observational data set. We haveapplied this technique to real observational data sets associated with theMilky Way, such as the luminosity function of satellite galaxies. A statisticalcomparison of model outputs and real observables is used to obtain a"best-fitting" parameter set. We consider different Milky Way-like dark matterhalos to account for the dependence of the best-fitting parameters selectionprocess on the underlying merger history of the models. For all formationhistories considered, running ChemTreeN with best-fitting parameters producedluminosity functions that tightly fit their observed counterpart. However, onlyone of the resulting stellar halo models was able to reproduce the observedstellar halo mass within 40 kpc of the Galactic center. On the basis of thisanalysis it is possible to disregard certain models, and their correspondingmerger histories, as good representations of the underlying merger history ofthe Milky Way.

Dissecting galaxy formation models with Sensitivity Analysis -- A new approach to constrain the Milky Way formation history