Mapping Variations of Redshift Distributions with Probability Integral Transforms

TL;DR

This paper introduces PITPZ, a novel method using probability integral transforms to accurately propagate uncertainties in galaxy redshift distributions, improving over traditional methods especially for calibration errors.

Contribution

The paper presents PITPZ, a new approach for mapping distribution variations that enhances uncertainty propagation in galaxy redshift measurements from imaging data.

Findings

PITPZ accurately estimates lensing amplitude uncertainty within 1% of the true value.

Traditional methods can underestimate uncertainty by up to 30%.

PITPZ is broadly applicable to uncertainty propagation problems.

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.