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While recent supernova cosmology research has benefited from improvedmeasurements, current analysis approaches are not statistically optimal andwill prove insufficient for future surveys. This paper discusses thelimitations of current supernova cosmological analyses in treating outliers,selection effects, shape- and color-standardization relations, unexplaineddispersion, and heterogeneous observations. We present a new Bayesianframework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY),that incorporates significant improvements in our ability to confront theseeffects. We apply the framework to real supernova observations and demonstratesmaller statistical and systematic uncertainties. We verify earlier resultsthat SNe Ia require nonlinear shape and color standardizations, but we nowinclude these nonlinear relations in a statistically well-justified way. Thisanalysis was primarily performed blinded, in that the basic framework was firstvalidated on simulated data before transitioning to real data. We also discusspossible extensions of the method.

UNITY: Confronting Supernova Cosmology's Statistical and Systematic Uncertainties in a Unified Bayesian Framework