Mapping Variations of Redshift Distributions with Probability Integral Transforms
Abstract
We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.
Cite
@article{arxiv.2210.03130,
title = {Mapping Variations of Redshift Distributions with Probability Integral Transforms},
author = {J. Myles and D. Gruen and A. Amon and A. Alarcon and J. DeRose and S. Everett and S. Dodelson and G. M. Bernstein and A. Campos and I. Harrison and N. MacCrann and J. McCullough and M. Raveri and C. Sánchez and M. A. Troxel and B. Yin and T. M. C. Abbott and S. Allam and O. Alves and F. Andrade-Oliveira and E. Bertin and D. Brooks and D. L. Burke and A. Carnero Rosell and M. Carrasco Kind and J. Carretero and R. Cawthon and M. Costanzi and L. N. da Costa and M. E. S. Pereira and S. Desai and P. Doel and I. Ferrero and B. Flaugher and J. Frieman and J. García-Bellido and M. Gatti and D. W. Gerdes and R. A. Gruendl and J. Gschwend and G. Gutierrez and W. G. Hartley and S. R. Hinton and D. L. Hollowood and K. Honscheid and D. J. James and K. Kuehn and O. Lahav and P. Melchior and J. Mena-Fernández and F. Menanteau and R. Miquel and J. J. Mohr and A. Palmese and F. Paz-Chinchón and A. Pieres and A. A. Plazas Malagón and J. Prat and M. Rodriguez-Monroy and E. Sanchez and V. Scarpine and I. Sevilla-Noarbe and M. Smith and E. Suchyta and M. E. C. Swanson and G. Tarle and D. L. Tucker and M. Vincenzi and N. Weaverdyck},
journal= {arXiv preprint arXiv:2210.03130},
year = {2023}
}