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Title: How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

A reliable estimate of the redshift distributionn(z) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo-z) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo-zpoint estimation. The established stacked estimator ofn(z) avoids reducing photo-zPDFs to point estimates but yields a systematically biased estimate ofn(z) that worsens with a decreasing signal-to-noise ratio, the very regime where photo-zPDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts (CHIPPR), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator ofn(z) produced by traditional procedures and is provably the only self-consistent way to recovern(z) from photo-zPDFs. We present thechipprprototype code, noting that the mathematically justifiable approach incurs computational cost. TheCHIPPRapproach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo-ztechniques, then the resulting posterior PDFs cannot be used for more » scientific inference. We therefore recommend that the photo-zcommunity focus on developing methodologies that enable the recovery of photo-zlikelihoods with support over all redshifts, either directly or via a known prior probability density.

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Publication Date:
Journal Name:
The Astrophysical Journal
Page Range or eLocation-ID:
Article No. 127
DOI PREFIX: 10.3847
Sponsoring Org:
National Science Foundation
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