Assessment of the Systematic Uncertainties in the Cosmological Analysis
  of the SDSS Supernovae Photometric Sample
  Improvement in the precision of measurements of cosmological parameters with
Type Ia Supernovae (SNIa) is expected to come from large photometrically
identified (photometric) SN samples. Here we re-analyse the SDSS photometric SN
sample, with roughly 700 high-quality, likely but unconfirmed SNIa
light-curves, to develop new analysis tools aimed at evaluating systematic
uncertainties on the dark energy equation-of-state parameter $w$. Since we
require a spectroscopically measured host galaxy redshift for each SN, we
determine the associated selection efficiency of host galaxies in order to
simulate bias corrections. We determine that the mis-association rate of host
galaxies is $0.6\%$; ignoring this effect in simulated bias corrections leads
to a $w$-bias of $\Delta w = +0.0007$, where $w$ is evaluated from SNIa and
priors from measurements of baryon acoustic oscillations and the cosmic
microwave background. We assess the uncertainty in our modeling of the host
galaxy selection efficiency and find the associated $w$ uncertainty to be
$-0.0072$. Finally, we explore new core collapse (CC) models in simulated
training samples and find that adjusting the CC luminosity distribution to be
in agreement with previous Pan-STARRS analyses yields a better match to the
SDSS data. The impact of ignoring this adjustment is $\Delta w = -0.0109$; the
impact of replacing the new CC models with those used by Pan-STARRS is $\Delta
w = -0.0028$. These systematic uncertainties are subdominant to the statistical
constraints from the SDSS sample, but must be considered in future photometric
analyses of large SN samples such as those from DES, LSST and WFIRST.
