Correcting Type Ia Supernova Distances for Selection Biases and
  Contamination in Photometrically Identified Samples
  We present a new technique to create a bin-averaged Hubble Diagram (HD) from
photometrically identified SN~Ia data. The resulting HD is corrected for
selection biases and contamination from core collapse (CC) SNe, and can be used
to infer cosmological parameters. This method, called "BBC" (BEAMS with Bias
Corrections), includes two fitting stages. The first BBC fitting stage uses a
posterior distribution that includes multiple SN likelihoods, a Monte Carlo
simulation to bias-correct the fitted SALT-II parameters, and CC probabilities
determined from a machine learning technique. The BBC fit determines 1) a
bin-averaged HD (average distance vs. redshift), and 2) the nuisance parameters
alpha and beta, which multiply the stretch and color (respectively) to
standardize the SN brightness. In the second stage, the bin-averaged HD is fit
to a cosmological model where priors can be imposed. We perform high precision
tests of the BBC method by simulating large (150,000 event) data samples
corresponding to the Dark Energy Survey Supernova Program. Our tests include
three models of intrinsic scatter, each with two different CC rates. In the BBC
fit, the SALT-II nuisance parameters alpha and beta are recovered to within 1%
of their true values. In the cosmology fit, we determine the dark energy
equation of state parameter w using a fixed value of Omega_matter as a prior:
averaging over all six tests based on 6 x 150,000 = 900,000 SNe, there is a
small w-bias of 0.006 +- 0.002. Finally, the BBC fitting code is publicly
available in the SNANA package.
