Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.
This content will become publicly available on July 29, 2024
We present posterior sample redshift distributions for the Hyper Suprime-Cam Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the galaxies’ photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of z < 1.2. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic and multiband photometric data that cover a spatial subset of the shear catalogue. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for sample redshift distributions of tomographic bins used in the three-year cosmological Weak Lensing analyses.
more » « less- Award ID(s):
- 2020295
- NSF-PAR ID:
- 10476080
- Publisher / Repository:
- Royal Astronomical Society
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 524
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 5109 to 5131
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract A reliable estimate of the redshift distribution
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-z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo-z point estimation. The established stacked estimator ofn (z ) avoids reducing photo-z PDFs 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-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 ofn (z ) produced by traditional procedures and is provably the only self-consistent way to recovern (z ) from photo-z PDFs. We present thechippr prototype code, noting that the mathematically justifiable approach incurs computational cost. TheCHIPPR 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-z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo-z community focus on developing methodologies that enable the recovery of photo-z likelihoods with support over all redshifts, either directly or via a known prior probability density.
