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

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.

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                    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

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                    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.

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@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}

}

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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