Estimating redshift distributions using hierarchical logistic Gaussian processes
Abstract
ABSTRACT This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10–30 per cent level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modelling biases.
- Authors:
-
- McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
- School of Computer Science and Statistics, Lloyd Institute, Trinity College, Dublin, Ireland
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1579995
- Grant/Contract Number:
- DESC0011114
- Resource Type:
- Published Article
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 491 Journal Issue: 4; Journal ID: ISSN 0035-8711
- Publisher:
- Oxford University Press
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Rau, Markus Michael, Wilson, Simon, and Mandelbaum, Rachel. Estimating redshift distributions using hierarchical logistic Gaussian processes. United Kingdom: N. p., 2019.
Web. doi:10.1093/mnras/stz3295.
Rau, Markus Michael, Wilson, Simon, & Mandelbaum, Rachel. Estimating redshift distributions using hierarchical logistic Gaussian processes. United Kingdom. doi:https://doi.org/10.1093/mnras/stz3295
Rau, Markus Michael, Wilson, Simon, and Mandelbaum, Rachel. Tue .
"Estimating redshift distributions using hierarchical logistic Gaussian processes". United Kingdom. doi:https://doi.org/10.1093/mnras/stz3295.
@article{osti_1579995,
title = {Estimating redshift distributions using hierarchical logistic Gaussian processes},
author = {Rau, Markus Michael and Wilson, Simon and Mandelbaum, Rachel},
abstractNote = {ABSTRACT This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10–30 per cent level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modelling biases.},
doi = {10.1093/mnras/stz3295},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 4,
volume = 491,
place = {United Kingdom},
year = {2019},
month = {11}
}
DOI: https://doi.org/10.1093/mnras/stz3295
Works referenced in this record:
Detection of Cosmic Magnification with the Sloan Digital Sky Survey
journal, November 2005
- Scranton, Ryan; Menard, Brice; Richards, Gordon T.
- The Astrophysical Journal, Vol. 633, Issue 2
Optimizing spectroscopic and photometric galaxy surveys: same-sky benefits for dark energy and modified gravity
journal, July 2015
- Kirk, Donnacha; Lahav, Ofer; Bridle, Sarah
- Monthly Notices of the Royal Astronomical Society, Vol. 451, Issue 4
Calibrating Redshift Distributions beyond Spectroscopic Limits with Cross‐Correlations
journal, September 2008
- Newman, Jeffrey A.
- The Astrophysical Journal, Vol. 684, Issue 1
CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions
journal, March 2013
- Benjamin, Jonathan; Van Waerbeke, Ludovic; Heymans, Catherine
- Monthly Notices of the Royal Astronomical Society, Vol. 431, Issue 2
ArborZ: PHOTOMETRIC REDSHIFTS USING BOOSTED DECISION TREES
journal, May 2010
- Gerdes, David W.; Sypniewski, Adam J.; McKay, Timothy A.
- The Astrophysical Journal, Vol. 715, Issue 2
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: angular clustering tomography and its cosmological implications
journal, March 2017
- Salazar-Albornoz, Salvador; Sánchez, Ariel G.; Grieb, Jan Niklas
- Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 3
Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey
journal, September 2006
- Ilbert, O.; Arnouts, S.; McCracken, H. J.
- Astronomy & Astrophysics, Vol. 457, Issue 3
On using angular cross-correlations to determine source redshift distributions
journal, July 2013
- McQuinn, M.; White, M.
- Monthly Notices of the Royal Astronomical Society, Vol. 433, Issue 4
Bayesian Multimodel Inference by RJMCMC: A Gibbs Sampling Approach
journal, August 2013
- Barker, Richard J.; Link, William A.
- The American Statistician, Vol. 67, Issue 3
Correcting cosmological parameter biases for all redshift surveys induced by estimating and reweighting redshift distributions
journal, December 2016
- Rau, Markus Michael; Hoyle, Ben; Paech, Kerstin
- Monthly Notices of the Royal Astronomical Society, Vol. 466, Issue 3
Spectroscopic failures in photometric redshift calibration: cosmological biases and survey requirements
journal, August 2014
- Cunha, Carlos E.; Huterer, Dragan; Lin, Huan
- Monthly Notices of the Royal Astronomical Society, Vol. 444, Issue 1
Reconstructing Redshift Distributions with Cross-Correlations: Tests and an Optimized Recipe
journal, August 2010
- Matthews, Daniel J.; Newman, Jeffrey A.
- The Astrophysical Journal, Vol. 721, Issue 1
Measuring photometric redshifts using galaxy images and Deep Neural Networks
journal, July 2016
- Hoyle, B.
- Astronomy and Computing, Vol. 16
Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model
journal, November 2018
- Sánchez, Carles; Bernstein, Gary M.
- Monthly Notices of the Royal Astronomical Society, Vol. 483, Issue 2
Catastrophic photometric redshift errors: weak-lensing survey requirements
journal, January 2010
- Bernstein, Gary; Huterer, Dragan
- Monthly Notices of the Royal Astronomical Society, Vol. 401, Issue 2
Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction
journal, January 2012
- Matthews, Daniel J.; Newman, Jeffrey A.
- The Astrophysical Journal, Vol. 745, Issue 2
GPz: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts
journal, July 2016
- Almosallam, Ibrahim A.; Jarvis, Matt J.; Roberts, Stephen J.
- Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 1
Modelling the angular correlation function and its full covariance in photometric galaxy surveys: Angular clustering in photometric surveys
journal, March 2011
- Crocce, Martín; Cabré, Anna; Gaztañaga, Enrique
- Monthly Notices of the Royal Astronomical Society, Vol. 414, Issue 1
Spectroscopic needs for imaging dark energy experiments
journal, March 2015
- Newman, Jeffrey A.; Abate, Alexandra; Abdalla, Filipe B.
- Astroparticle Physics, Vol. 63
Bayesian photometric redshifts of blended sources
journal, December 2018
- Jones, Daniel M.; Heavens, Alan F.
- Monthly Notices of the Royal Astronomical Society, Vol. 483, Issue 2
Clustering-based redshift estimation: application to VIPERS/CFHTLS
journal, July 2016
- Scottez, V.; Mellier, Y.; Granett, B. R.
- Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 2
The angular power spectra of photometric Sloan Digital Sky Survey luminous red galaxies: The angular power spectra of photometric LRGs
journal, February 2011
- Thomas, Shaun A.; Abdalla, Filipe B.; Lahav, Ofer
- Monthly Notices of the Royal Astronomical Society, Vol. 412, Issue 3
How accurate is Limber's equation?
journal, August 2007
- Simon, P.
- Astronomy & Astrophysics, Vol. 473, Issue 3
The Dark Energy Survey: Data Release 1
journal, November 2018
- Abbott, T. M. C.; Abdalla, F. B.; Allam, S.
- The Astrophysical Journal Supplement Series, Vol. 239, Issue 2
Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
journal, June 2016
- Leistedt, Boris; Mortlock, Daniel J.; Peiris, Hiranya V.
- Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 4
Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North
journal, December 1999
- Arnouts, S.; Cristiani, S.; Moscardini, L.
- Monthly Notices of the Royal Astronomical Society, Vol. 310, Issue 2
Cosmological constraints with clustering-based redshifts
journal, March 2017
- Kovetz, Ely D.; Raccanelli, Alvise; Rahman, Mubdi
- Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 3
The Hyper Suprime-Cam SSP Survey: Overview and survey design
journal, September 2017
- Aihara, Hiroaki; Arimoto, Nobuo; Armstrong, Robert
- Publications of the Astronomical Society of Japan, Vol. 70, Issue SP1
Using neural networks to estimate redshift distributions. An application to CFHTLenS
journal, March 2015
- Bonnett, Christopher
- Monthly Notices of the Royal Astronomical Society, Vol. 449, Issue 1
TPZ: photometric redshift PDFs and ancillary information by using prediction trees and random forests
journal, May 2013
- Carrasco Kind, Matias; Brunner, Robert J.
- Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 2
Data augmentation for machine learning redshifts applied to Sloan Digital Sky Survey galaxies
journal, April 2015
- Hoyle, Ben; Rau, Markus Michael; Bonnett, Christopher
- Monthly Notices of the Royal Astronomical Society, Vol. 450, Issue 1
Photometric redshifts and model spectral energy distributions of galaxies from the SDSS-III BOSS DR10 data
journal, June 2015
- Greisel, N.; Seitz, S.; Drory, N.
- Monthly Notices of the Royal Astronomical Society, Vol. 451, Issue 2
Dark Energy Survey Year 1 results: cross-correlation redshifts – methods and systematics characterization
journal, February 2018
- Gatti, M.; Vielzeuf, P.; Davis, C.
- Monthly Notices of the Royal Astronomical Society, Vol. 477, Issue 2
Accurate photometric redshift probability density estimation – method comparison and application
journal, August 2015
- Rau, Markus Michael; Seitz, Stella; Brimioulle, Fabrice
- Monthly Notices of the Royal Astronomical Society, Vol. 452, Issue 4
Galaxy Clustering in Early Sloan Digital Sky Survey Redshift Data
journal, May 2002
- Zehavi, Idit; Blanton, Michael R.; Frieman, Joshua A.
- The Astrophysical Journal, Vol. 571, Issue 1
Bayesian Photometric Redshift Estimation
journal, June 2000
- Benitez, Narciso
- The Astrophysical Journal, Vol. 536, Issue 2
ANN z : Estimating Photometric Redshifts Using Artificial Neural Networks
journal, April 2004
- Collister, Adrian A.; Lahav, Ofer
- Publications of the Astronomical Society of the Pacific, Vol. 116, Issue 818
A joint analysis for cosmology and photometric redshift calibration using cross-correlations
journal, November 2016
- McLeod, Michael; Balan, Sreekumar T.; Abdalla, Filipe B.
- Monthly Notices of the Royal Astronomical Society, Vol. 466, Issue 3
2dFLenS and KiDS: determining source redshift distributions with cross-correlations
journal, November 2016
- Johnson, Andrew; Blake, Chris; Amon, Alexandra
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 4
Effects of Photometric Redshift Uncertainties on Weak‐Lensing Tomography
journal, January 2006
- Ma, Zhaoming; Hu, Wayne; Huterer, Dragan
- The Astrophysical Journal, Vol. 636, Issue 1
Weak Lensing for Precision Cosmology
journal, September 2018
- Mandelbaum, Rachel
- Annual Review of Astronomy and Astrophysics, Vol. 56, Issue 1
LSST: From Science Drivers to Reference Design and Anticipated Data Products
journal, March 2019
- Ivezić, Željko; Kahn, Steven M.; Tyson, J. Anthony
- The Astrophysical Journal, Vol. 873, Issue 2
First results from the IllustrisTNG simulations: matter and galaxy clustering
journal, December 2017
- Springel, Volker; Pakmor, Rüdiger; Pillepich, Annalisa
- Monthly Notices of the Royal Astronomical Society, Vol. 475, Issue 1
CosmoSIS: Modular cosmological parameter estimation
journal, September 2015
- Zuntz, J.; Paterno, M.; Jennings, E.
- Astronomy and Computing, Vol. 12
KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing
journal, November 2016
- Hildebrandt, H.; Viola, M.; Heymans, C.
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 2
Dark Energy Survey Year 1 Results: redshift distributions of the weak-lensing source galaxies
journal, April 2018
- Hoyle, B.; Gruen, D.; Bernstein, G. M.
- Monthly Notices of the Royal Astronomical Society, Vol. 478, Issue 1
Bayesian measures of model complexity and fit
journal, October 2002
- Spiegelhalter, David J.; Best, Nicola G.; Carlin, Bradley P.
- Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 64, Issue 4
The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field.
journal, January 1953
- Limber, D. Nelson
- The Astrophysical Journal, Vol. 117
The Zurich Extragalactic Bayesian Redshift Analyzer and its first application: COSMOS
journal, October 2006
- Feldmann, R.; Carollo, C. M.; Porciani, C.
- Monthly Notices of the Royal Astronomical Society, Vol. 372, Issue 2