Cosmology with Photometric Surveys of Type Ia Supernovae
  We discuss the extent to which photometric measurements alone can be used to
identify Type Ia supernovae (SNIa) and to determine redshift and other
parameters of interest for cosmological studies. We fit the light curve data of
the type expected from a survey such as the one planned with Large Synoptic
Survey Telescope (LSST) and also to remove the contamination from the
core-collapse supernovae to SNIa samples. We generate 1000 SNIa mock flux data
for each of the LSST filters based on existing design parameters, then use a
Markov Chain Monte-Carlo (MCMC) analysis to fit for the redshift, apparent
magnitude, stretch factor and the phase of the SNIa. We find that the model
fitting works adequately well when the true SNe redshift is below 0.5, while at
$z < 0.2$ the accuracy of the photometric data is almost comparable with
spectroscopic measurements of the same sample. We discuss the contamination of
Type Ib/c (SNIb/c) and Type II supernova (SNII) on the SNIa data set. We find
it is easy to distinguish the SNII through the large $\chi^2$ mismatch when
fitting to photometric data with Ia light curves. This is not the case for
SNIb/c. We implement a statistical method based on the Bayesian estimation in
order to statistically reduce the contamination from SNIb/c for cosmological
parameter measurements from the whole SNe sample. The proposed statistical
method also evaluate the fraction of the SNIa in the total SNe data set, which
provides a valuable guide to establish the degree of contamination.
