RUB » Bibliotheksportal

Alex I. Malz, David W. Hogg

• A reliable estimate of the redshift distribution \(\textit {n(z)}\) 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-\(\it z\)) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo-\(\it z\) point estimation. The established stacked estimator of \(\textit {n(z)}\) avoids reducing photo-\(\it z\) PDFs to point estimates but yields a systematically biased estimate of \(\textit {n(z)}\) that worsens with a decreasing signal-to-noise ratio, the very regime where photo-\(\it z\) PDFs 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 of \(\textit {n(z)}\) produced by traditional procedures and is provably the only self-consistent way to recover \(\textit {n(z)}\) from photo-\(\it z\) PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach 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-\(\it z\) techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo-\(\it z\) community focus on developing methodologies that enable the recovery of photo-\(\it z\) likelihoods with support over all redshifts, either directly or via a known prior probability density.