Using MiniBooNE NCEL and CCQE cross section results to constrain 3+1 sterile neutrino models

The MiniBooNE NCEL and CCQE cross-section measurements (neutrino running) are used to set limits in the $\Delta m^{2}-\sin^{2}\vartheta_{\mu s}$ plane for a 3+1 sterile neutrino model with a mass splitting $0.1 \leq \Delta m^{2} \leq 10.0$ eV$^{2}$. GENIE is used, with a relativistic Fermi gas model, to relate $E_{\nu}$ and the reconstructed quantities measured. The issue of uncertainty in the underlying cross-section model and its effect on the sterile neutrino limits is explored, and robust sterile neutrino limits are produced by fitting the sterile parameters and the axial-mass cross-section parameter simultaneously.