with $\theta_{\mu} > 20^{\circ}$ is very low because the MINOS near detector, downstream of [MINER$\nu$A]{}, is used to tag muons. This introduces a small model dependence on the results because an RFG model was used to correct for the unsampled region of phase-space. The [MINER$\nu$A]{}collaboration subsequently released a distribution where the cross section is measured for CCQE events with $\theta_{\mu} \leq 20^{\circ}$. As this dataset is less model-dependent, it has been used in the fits, and will be consistently used in this analysis. [MINER$\nu$A]{}also made cross-correlations between the neutrino and antineutrino datasets available in a data release after the publication of their CCQE papers. The correlation matrices released include both shape and normalization errors, but it is possible to extract shape-only correlation matrices using the method given in Reference [@teppeiThesis]. The full matrix including both shape and normalization errors included is shown in Figure \[fig:cross-correlation\].

![Cross-correlation matrix including both shape and normalization uncertainties for the [MINER$\nu$A]{}neutrino and antineutrino samples. The eight neutrino and eight antineutrino bins shown here correspond to the eight [$Q^{2}_{\textrm{QE}}$]{}bins from the [MINER$\nu$A]{}datasets.[]{data-label="fig:cross-correlation"}](figures/MINERvA_cross-correlations.pdf){width="0.9\columnwidth"}

Monte Carlo prediction {#sec:mcpred}
======================

For each of the four experimental results included in the fit, one million CCQE and 2p2h events were generated 