Estimating redshift distributions using hierarchical logistic Gaussian processes

Rau, Markus Michael; Wilson, Simon; Mandelbaum, Rachel

doi:10.1093/mnras/stz3295

Title: 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:

^[1]; Wilson, Simon ^[2];

^[1]

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:: 2019-11-26

Research Org.:: Carnegie Mellon Univ., Pittsburgh, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1579995

Alternate Identifier(s):: OSTI ID: 1802211

Grant/Contract Number:: DESC0011114; SC0011114

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

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; catalogues; surveys; galaxies: distances and redshifts

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.

Copy to clipboard


                    Rau, Markus Michael, Wilson, Simon, & Mandelbaum, Rachel. Estimating redshift distributions using hierarchical logistic Gaussian processes.  United Kingdom.  https://doi.org/10.1093/mnras/stz3295

Copy to clipboard


                    Rau, Markus Michael, Wilson, Simon, and Mandelbaum, Rachel. Tue .  
"Estimating redshift distributions using hierarchical logistic Gaussian processes".  United Kingdom.  https://doi.org/10.1093/mnras/stz3295.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1093/mnras/stz3295

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

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
DOI: 10.1086/431358

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
DOI: 10.1093/mnras/stv1268

Calibrating Redshift Distributions beyond Spectroscopic Limits with Cross‐Correlations
journal, September 2008

Newman, Jeffrey A.
The Astrophysical Journal, Vol. 684, Issue 1
DOI: 10.1086/589982

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
DOI: 10.1093/mnras/stt276

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
DOI: 10.1088/0004-637X/715/2/823

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
DOI: 10.1093/mnras/stx633

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
DOI: 10.1051/0004-6361:20065138

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
DOI: 10.1093/mnras/stt914

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
DOI: 10.1080/00031305.2013.791644

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
DOI: 10.1093/mnras/stw3338

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
DOI: 10.1093/mnras/stu1424

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
DOI: 10.1088/0004-637X/721/1/456

Measuring photometric redshifts using galaxy images and Deep Neural Networks
journal, July 2016

Hoyle, B.
Astronomy and Computing, Vol. 16
DOI: 10.1016/j.ascom.2016.03.006

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
DOI: 10.1093/mnras/sty3222

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
DOI: 10.1111/j.1365-2966.2009.15748.x

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
DOI: 10.1088/0004-637X/745/2/180

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
DOI: 10.1093/mnras/stw1618

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
DOI: 10.1111/j.1365-2966.2011.18393.x

Spectroscopic needs for imaging dark energy experiments
journal, March 2015

Newman, Jeffrey A.; Abate, Alexandra; Abdalla, Filipe B.
Astroparticle Physics, Vol. 63
DOI: 10.1016/j.astropartphys.2014.06.007

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
DOI: 10.1093/mnras/sty3279

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
DOI: 10.1093/mnras/stw1500

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
DOI: 10.1111/j.1365-2966.2010.18004.x

How accurate is Limber's equation?
journal, August 2007

Simon, P.
Astronomy & Astrophysics, Vol. 473, Issue 3
DOI: 10.1051/0004-6361:20066352

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
DOI: 10.3847/1538-4365/aae9f0

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
DOI: 10.1093/mnras/stw1304

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
DOI: 10.1046/j.1365-8711.1999.02978.x

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
DOI: 10.1093/mnras/stx691

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
DOI: 10.1093/pasj/psx066

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
DOI: 10.1093/mnras/stv230

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
DOI: 10.1093/mnras/stt574

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
DOI: 10.1093/mnras/stv599

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
DOI: 10.1093/mnras/stv1005

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
DOI: 10.1093/mnras/sty466

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
DOI: 10.1093/mnras/stv1567

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
DOI: 10.1086/339893

Bayesian Photometric Redshift Estimation
journal, June 2000

Benitez, Narciso
The Astrophysical Journal, Vol. 536, Issue 2
DOI: 10.1086/308947

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
DOI: 10.1086/383254

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
DOI: 10.1093/mnras/stw2989

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
DOI: 10.1093/mnras/stw3033

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
DOI: 10.1086/497068

Weak Lensing for Precision Cosmology
journal, September 2018

Mandelbaum, Rachel
Annual Review of Astronomy and Astrophysics, Vol. 56, Issue 1
DOI: 10.1146/annurev-astro-081817-051928

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
DOI: 10.3847/1538-4357/ab042c

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
DOI: 10.1093/mnras/stx3304

CosmoSIS: Modular cosmological parameter estimation
journal, September 2015

Zuntz, J.; Paterno, M.; Jennings, E.
Astronomy and Computing, Vol. 12
DOI: 10.1016/j.ascom.2015.05.005

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
DOI: 10.1093/mnras/stw2805

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
DOI: 10.1093/mnras/sty957

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
DOI: 10.1111/1467-9868.00353

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
DOI: 10.1086/145672

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
DOI: 10.1111/j.1365-2966.2006.10930.x

Similar Records in DOE PAGES and OSTI.GOV collections:

Self-consistent redshift estimation using correlation functions without a spectroscopic reference sample

Journal Article Hoyle, Ben ; Rau, Markus Michael - Monthly Notices of the Royal Astronomical Society

ABSTRACT We present a new method to estimate redshift distributions and galaxy-dark matter bias parameters using correlation functions in a fully data driven and self-consistent manner. Unlike other machine learning, template, or correlation redshift methods, this approach does not require a reference sample with known redshifts. By measuring the projected cross- and auto-correlations of different galaxy sub-samples, e.g. as chosen by simple cells in colour–magnitude space, we are able to estimate the galaxy-dark matter bias model parameters, and the shape of the redshift distributions of each sub-sample. This method fully marginalizes over a flexible parametrization of the redshift distribution andmore »« less
Cited by 1
https://doi.org/10.1093/mnras/stz502
Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model – Application to realistic N -body simulations

Journal Article Alarcon, Alex ; Sánchez, Carles ; Bernstein, Gary M. ; ... - Monthly Notices of the Royal Astronomical Society

ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift ofmore »« less
https://doi.org/10.1093/mnras/staa2478
Cross-correlation redshift calibration without spectroscopic calibration samples in DES Science Verification Data

Journal Article Davis, C. ; Rozo, E. ; Roodman, A. ; ... - Monthly Notices of the Royal Astronomical Society

Galaxy cross-correlations with high-fidelity redshift samples hold the potential to precisely calibrate systematic photometric redshift uncertainties arising from the unavailability of complete and representative training and validation samples of galaxies. However, application of this technique in the Dark Energy Survey (DES) is hampered by the relatively low number density, small area, and modest redshift overlap between photometric and spectroscopic samples. We propose instead using photometric catalogues with reliable photometric redshifts for photo-z calibration via cross-correlations. We verify the viability of our proposal using redMaPPer clusters from the Sloan Digital Sky Survey (SDSS) to successfully recover the redshift distribution of SDSSmore »« less
Cited by 6
https://doi.org/10.1093/mnras/sty787

Full Text Available
Dark Energy Survey Year 1 results: cross-correlation redshifts – methods and systematics characterization

Journal Article Gatti, M. ; Vielzeuf, P. ; Davis, C. ; ... - Monthly Notices of the Royal Astronomical Society

We use numerical simulations to characterize the performance of a clustering-based method to calibrate photometric redshift biases. In particular, we cross-correlate the weak lensing source galaxies from the Dark Energy Survey Year 1 sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) to estimate the redshift distribution of the former sample. The recovered redshift distributions are used to calibrate the photometric redshift bias of standard photo-z methods applied to the same source galaxy sample.We apply the method to two photo-z codes run in our simulated data: Bayesian Photometric Redshift and Directional Neighbourhood Fitting. We characterize the systematic uncertaintiesmore »« less
Cited by 14
https://doi.org/10.1093/mnras/sty466

Full Text Available
A GENERAL STUDY OF THE INFLUENCE OF CATASTROPHIC PHOTOMETRIC REDSHIFT ERRORS ON COSMOLOGY WITH COSMIC SHEAR TOMOGRAPHY

Journal Article Hearin, Andrew P ; Zentner, Andrew R ; Zhaoming, Ma ; ... - Astrophysical Journal

A goal of forthcoming imaging surveys is to use weak gravitational lensing shear measurements to constrain dark energy. A challenge to this program is that redshifts to the lensed, source galaxies must be determined using photometric, rather than spectroscopic, information. We quantify the importance of uncalibrated photometric redshift outliers to the dark energy goals of forthcoming imaging surveys in a manner that does not assume any particular photometric redshift technique or template. In so doing, we provide an approximate blueprint for computing the influence of specific outlier populations on dark energy constraints. We find that outlier populations whose photo-z distributionsmore »« less
https://doi.org/10.1088/0004-637X/720/2/1351

Similar Records

Title: Estimating redshift distributions using hierarchical logistic Gaussian processes

Abstract

Citation Formats

Detection of Cosmic Magnification with the Sloan Digital Sky Survey journal, November 2005

Optimizing spectroscopic and photometric galaxy surveys: same-sky benefits for dark energy and modified gravity journal, July 2015

Calibrating Redshift Distributions beyond Spectroscopic Limits with Cross‐Correlations journal, September 2008

CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions journal, March 2013

ArborZ: PHOTOMETRIC REDSHIFTS USING BOOSTED DECISION TREES journal, May 2010

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: angular clustering tomography and its cosmological implications journal, March 2017

Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey journal, September 2006

On using angular cross-correlations to determine source redshift distributions journal, July 2013

Bayesian Multimodel Inference by RJMCMC: A Gibbs Sampling Approach journal, August 2013

Correcting cosmological parameter biases for all redshift surveys induced by estimating and reweighting redshift distributions journal, December 2016

Spectroscopic failures in photometric redshift calibration: cosmological biases and survey requirements journal, August 2014

Reconstructing Redshift Distributions with Cross-Correlations: Tests and an Optimized Recipe journal, August 2010

Measuring photometric redshifts using galaxy images and Deep Neural Networks journal, July 2016

Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model journal, November 2018

Catastrophic photometric redshift errors: weak-lensing survey requirements journal, January 2010

Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction journal, January 2012

GPz: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts journal, July 2016

Modelling the angular correlation function and its full covariance in photometric galaxy surveys: Angular clustering in photometric surveys journal, March 2011

Spectroscopic needs for imaging dark energy experiments journal, March 2015

Bayesian photometric redshifts of blended sources journal, December 2018

Clustering-based redshift estimation: application to VIPERS/CFHTLS journal, July 2016

The angular power spectra of photometric Sloan Digital Sky Survey luminous red galaxies: The angular power spectra of photometric LRGs journal, February 2011

How accurate is Limber's equation? journal, August 2007

The Dark Energy Survey: Data Release 1 journal, November 2018

Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys journal, June 2016

Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North journal, December 1999

Cosmological constraints with clustering-based redshifts journal, March 2017

The Hyper Suprime-Cam SSP Survey: Overview and survey design journal, September 2017

Using neural networks to estimate redshift distributions. An application to CFHTLenS journal, March 2015

TPZ: photometric redshift PDFs and ancillary information by using prediction trees and random forests journal, May 2013

Data augmentation for machine learning redshifts applied to Sloan Digital Sky Survey galaxies journal, April 2015

Photometric redshifts and model spectral energy distributions of galaxies from the SDSS-III BOSS DR10 data journal, June 2015

Dark Energy Survey Year 1 results: cross-correlation redshifts – methods and systematics characterization journal, February 2018

Accurate photometric redshift probability density estimation – method comparison and application journal, August 2015

Galaxy Clustering in Early Sloan Digital Sky Survey Redshift Data journal, May 2002

Bayesian Photometric Redshift Estimation journal, June 2000

ANN z : Estimating Photometric Redshifts Using Artificial Neural Networks journal, April 2004

A joint analysis for cosmology and photometric redshift calibration using cross-correlations journal, November 2016

2dFLenS and KiDS: determining source redshift distributions with cross-correlations journal, November 2016

Effects of Photometric Redshift Uncertainties on Weak‐Lensing Tomography journal, January 2006

Weak Lensing for Precision Cosmology journal, September 2018

LSST: From Science Drivers to Reference Design and Anticipated Data Products journal, March 2019

First results from the IllustrisTNG simulations: matter and galaxy clustering journal, December 2017

CosmoSIS: Modular cosmological parameter estimation journal, September 2015

KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing journal, November 2016

Dark Energy Survey Year 1 Results: redshift distributions of the weak-lensing source galaxies journal, April 2018

Bayesian measures of model complexity and fit journal, October 2002

The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field. journal, January 1953

The Zurich Extragalactic Bayesian Redshift Analyzer and its first application: COSMOS journal, October 2006

Detection of Cosmic Magnification with the Sloan Digital Sky Survey
journal, November 2005

Optimizing spectroscopic and photometric galaxy surveys: same-sky benefits for dark energy and modified gravity
journal, July 2015

Calibrating Redshift Distributions beyond Spectroscopic Limits with Cross‐Correlations
journal, September 2008

CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions
journal, March 2013

ArborZ: PHOTOMETRIC REDSHIFTS USING BOOSTED DECISION TREES
journal, May 2010

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: angular clustering tomography and its cosmological implications
journal, March 2017

Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey
journal, September 2006

On using angular cross-correlations to determine source redshift distributions
journal, July 2013

Bayesian Multimodel Inference by RJMCMC: A Gibbs Sampling Approach
journal, August 2013

Correcting cosmological parameter biases for all redshift surveys induced by estimating and reweighting redshift distributions
journal, December 2016

Spectroscopic failures in photometric redshift calibration: cosmological biases and survey requirements
journal, August 2014

Reconstructing Redshift Distributions with Cross-Correlations: Tests and an Optimized Recipe
journal, August 2010

Measuring photometric redshifts using galaxy images and Deep Neural Networks
journal, July 2016

Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model
journal, November 2018

Catastrophic photometric redshift errors: weak-lensing survey requirements
journal, January 2010

Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction
journal, January 2012

GPz: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts
journal, July 2016

Modelling the angular correlation function and its full covariance in photometric galaxy surveys: Angular clustering in photometric surveys
journal, March 2011

Spectroscopic needs for imaging dark energy experiments
journal, March 2015

Bayesian photometric redshifts of blended sources
journal, December 2018

Clustering-based redshift estimation: application to VIPERS/CFHTLS
journal, July 2016

The angular power spectra of photometric Sloan Digital Sky Survey luminous red galaxies: The angular power spectra of photometric LRGs
journal, February 2011

How accurate is Limber's equation?
journal, August 2007

The Dark Energy Survey: Data Release 1
journal, November 2018

Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
journal, June 2016

Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North
journal, December 1999

Cosmological constraints with clustering-based redshifts
journal, March 2017

The Hyper Suprime-Cam SSP Survey: Overview and survey design
journal, September 2017

Using neural networks to estimate redshift distributions. An application to CFHTLenS
journal, March 2015

TPZ: photometric redshift PDFs and ancillary information by using prediction trees and random forests
journal, May 2013

Data augmentation for machine learning redshifts applied to Sloan Digital Sky Survey galaxies
journal, April 2015

Photometric redshifts and model spectral energy distributions of galaxies from the SDSS-III BOSS DR10 data
journal, June 2015

Dark Energy Survey Year 1 results: cross-correlation redshifts – methods and systematics characterization
journal, February 2018

Accurate photometric redshift probability density estimation – method comparison and application
journal, August 2015

Galaxy Clustering in Early Sloan Digital Sky Survey Redshift Data
journal, May 2002

Bayesian Photometric Redshift Estimation
journal, June 2000

ANN z : Estimating Photometric Redshifts Using Artificial Neural Networks
journal, April 2004

A joint analysis for cosmology and photometric redshift calibration using cross-correlations
journal, November 2016

2dFLenS and KiDS: determining source redshift distributions with cross-correlations
journal, November 2016

Effects of Photometric Redshift Uncertainties on Weak‐Lensing Tomography
journal, January 2006

Weak Lensing for Precision Cosmology
journal, September 2018

LSST: From Science Drivers to Reference Design and Anticipated Data Products
journal, March 2019

First results from the IllustrisTNG simulations: matter and galaxy clustering
journal, December 2017

CosmoSIS: Modular cosmological parameter estimation
journal, September 2015

KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing
journal, November 2016

Dark Energy Survey Year 1 Results: redshift distributions of the weak-lensing source galaxies
journal, April 2018

Bayesian measures of model complexity and fit
journal, October 2002

The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field.
journal, January 1953

The Zurich Extragalactic Bayesian Redshift Analyzer and its first application: COSMOS
journal, October 2006