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Recent cosmological analyses (e.g., JLA, Pantheon) of Type Ia Supernova(SNIa) have propagated systematic uncertainties into a covariance matrix andeither binned or smoothed the systematic vectors in redshift space. Wedemonstrate that systematic error budgets of these analyses can be improved bya factor of $\sim1.5\times$ with the use of unbinned and unsmoothed covariancematrices. To understand this, we employ a separate approach that simultaneouslyfits for cosmological parameters and additional self-calibrating scaleparameters that constrain the size of each systematic. We show that thecovariance-matrix approach and scale-parameter approach yield equivalentresults, implying that in both cases the data can self-calibrate certainsystematic uncertainties, but that this ability is hindered when information isbinned or smoothed in redshift space. We review the top systematicuncertainties in current analyses and find that the reduction of systematicuncertainties in the unbinned case depends on whether a systematic isconsistent with varying the cosmological model and whether or not thesystematic can be described by additional correlations between SN propertiesand luminosity. Furthermore, we show that the power of self-calibrationincreases with the size of the dataset, which presents a tremendous opportunityfor upcoming analyses of photometrically classified samples, like those ofLegacy Survey of Space and Time (LSST) and the Nancy Grace Roman Telescope(NGRST). However, to take advantage of self-calibration in large,photometrically-classified samples, we must first address the issue thatbinning is required in currently-used photometric methodologies.

Binning is Sinning (Supernova Version): The Impact of Self-Calibration in Cosmological Analyses with Type Ia Supernovae