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We present a new technique to create a bin-averaged Hubble Diagram (HD) fromphotometrically identified SN~Ia data. The resulting HD is corrected forselection biases and contamination from core collapse (CC) SNe, and can be usedto infer cosmological parameters. This method, called "BBC" (BEAMS with BiasCorrections), includes two fitting stages. The first BBC fitting stage uses aposterior distribution that includes multiple SN likelihoods, a Monte Carlosimulation to bias-correct the fitted SALT-II parameters, and CC probabilitiesdetermined from a machine learning technique. The BBC fit determines 1) abin-averaged HD (average distance vs. redshift), and 2) the nuisance parametersalpha and beta, which multiply the stretch and color (respectively) tostandardize the SN brightness. In the second stage, the bin-averaged HD is fitto a cosmological model where priors can be imposed. We perform high precisiontests of the BBC method by simulating large (150,000 event) data samplescorresponding to the Dark Energy Survey Supernova Program. Our tests includethree models of intrinsic scatter, each with two different CC rates. In the BBCfit, 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 energyequation 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 asmall w-bias of 0.006 +- 0.002. Finally, the BBC fitting code is publiclyavailable in the SNANA package.

Correcting Type Ia Supernova Distances for Selection Biases and Contamination in Photometrically Identified Samples