  A number of short baseline neutrino oscillation experiments have observed an
anomalous excess of neutrinos in the low energy range. This may hint towards
the existence of additional neutrino mass splittings. If true, additional
sterile (non-interacting) neutrino states above the current 3 neutrino model
would be required. On the other hand, many parameters of the allowed space are
limited by experiments that have seen no anomaly. We will introduce models
which accommodate these additional neutrinos, and then discuss our work towards
fitting these models to the available global high $\Delta m^{2}$ oscillation
data. We will then present the latest results of these fits.
