Re-calibrating Photometric Redshift Probability Distributions Using Feature-space Regression
This addresses systematic errors in redshift estimates for astrophysical analyses, though it is incremental as it builds on existing global calibration methods.
The paper tackles the problem of inaccurate photometric redshift probability distributions in astrophysics, which cause systematic errors, by introducing a local re-calibration method using feature-space regression to ensure these distributions meet frequentist definitions, resulting in calibrated PDFs across all feature space locations.
Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors. However, probability distribution outputs from many photometric redshift methods do not follow the frequentist definition of a Probability Density Function (PDF) for redshift -- i.e., the fraction of times the true redshift falls between two limits $z_{1}$ and $z_{2}$ should be equal to the integral of the PDF between these limits. Previous works have used the global distribution of Probability Integral Transform (PIT) values to re-calibrate PDFs, but offsetting inaccuracies in different regions of feature space can conspire to limit the efficacy of the method. We leverage a recently developed regression technique that characterizes the local PIT distribution at any location in feature space to perform a local re-calibration of photometric redshift PDFs. Though we focus on an example from astrophysics, our method can produce PDFs which are calibrated at all locations in feature space for any use case.