Analytic marginalization of $N(z)$ uncertainties in tomographic galaxy surveys

Abstract

We present a new method to marginalize over uncertainties in redshift distributions, $N(z)$, within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess $N(z)$ governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample-variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.

26 pages, 7 figures

References in corpus (6)

• Calibrating Redshift Distributions Beyond Spectroscopic Limits with Cross-Correlations
• Photometric Redshift Calibration with Self Organising Maps
• On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods
• Redshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model $-$ Application to realistic $N$-body simulations
• Beware of commonly used approximations I: errors in forecasts
• Propagating sample variance uncertainties in redshift calibration: simulations, theory and application to the COSMOS2015 data

Cited by in corpus (13)

• Cosmological constraints from unWISE and Planck CMB lensing tomography
• Dark Energy Survey Year 3 results: Marginalisation over redshift distribution uncertainties using ranking of discrete realisations
• Photo-z outlier self-calibration in weak lensing surveys
• Self-calibration and robust propagation of photometric redshift distribution uncertainties in weak gravitational lensing
• Photometric Redshift Uncertainties in Weak Gravitational Lensing Shear Analysis: Models and Marginalization
• A Composite Likelihood Approach for Inference under Photometric Redshift Uncertainty
• Analytical marginalisation over photometric redshift uncertainties in cosmic shear analyses
• Euclid: Calibrating photometric redshifts with spectroscopic cross-correlations
• Combining cosmic shear data with correlated photo-$z$ uncertainties: constraints from DESY1 and HSC-DR1
• Mapping Variations of Redshift Distributions with Probability Integral Transforms
• Impact of redshift distribution uncertainties on Lyman-break galaxy cosmological parameter inference
• The invariance of group occupation across the cosmic web
• Improving Photometric Galaxy Clustering Constraints With Cross-Bin Correlations