Exhausting the Information: Novel Bayesian Combination of Photometric Redshift PDFs

The estimation and utilization of photometric redshift probability density functions (photo-z PDFs) has become increasingly important over the last few years. Primarily this is because of the prominent role photo-z PDFs play in enabling photometric survey data to be used to make cosmological constraints, especially when compared to single photo-z estimates. Currently there exist a wide variety of algorithms to compute photo-z ’s, each with their own strengths and weaknesses. In this paper, we present a novel and ecient Bayesian framework that combines the results from dierent photoz techniques into a more powerful and robust estimate by maximizing the information from the photometric data. To demonstrate this we use a supervised machine learning technique based on prediction trees and a random forest, an unsupervised method based on self organizing maps and a random atlas, and a standard template tting method but can be easily extend

[1]  D. Gerdes,et al.  PHAT: PHoto-z Accuracy Testing , 2010, 1008.0658.

[2]  Alison L. Coil,et al.  The DEIMOS spectrograph for the Keck II Telescope: integration and testing , 2003, SPIE Astronomical Telescopes + Instrumentation.

[3]  T. Loredo,et al.  A new method for the detection of a periodic signal of unknown shape and period , 1992 .

[4]  Andrew R. Liddle,et al.  Bayesian model averaging in astrophysics: a review , 2013, Stat. Anal. Data Min..

[5]  Jiangang Hao,et al.  ArborZ: PHOTOMETRIC REDSHIFTS USING BOOSTED DECISION TREES , 2009, The Astrophysical Journal.

[6]  A. Fontana,et al.  A CRITICAL ASSESSMENT OF PHOTOMETRIC REDSHIFT METHODS: A CANDELS INVESTIGATION , 2013, 1308.5353.

[7]  R. J. Brunner,et al.  Sparse representation of photometric redshift probability density functions: preparing for petascale astronomy , 2014, 1404.6442.

[8]  J. Frieman,et al.  Photometric Redshift Error Estimators , 2007, 0711.0962.

[9]  Karl Glazebrook,et al.  The WiggleZ Dark Energy Survey: survey design and first data release , 2009, 0911.4246.

[10]  Y. Wadadekar.  Estimating Photometric Redshifts Using Support Vector Machines , 2004, astro-ph/0412005.

[11]  Stefan Hilbert,et al.  COSMIC SHEAR RESULTS FROM THE DEEP LENS SURVEY. I. JOINT CONSTRAINTS ON ΩM AND σ8 WITH A TWO-DIMENSIONAL ANALYSIS , 2012, 1210.2732.

[12]  Nicholas M. Ball,et al.  Incorporating photometric redshift probability density information into real-space clustering measurements , 2009, 0903.3121.

[13]  S. Gwyn,et al.  The CFHT Legacy Survey: stacked images and catalogs , 2011, 1101.1084.

[14]  Tony R. Martinez,et al.  Turning Bayesian model averaging into Bayesian model combination , 2011, The 2011 International Joint Conference on Neural Networks.

[15]  Astronomy,et al.  Photometric Redshift Estimation Using Spectral Connectivity Analysis , 2009, 0906.0995.

[16]  R. J. Assef,et al.  Low Resolution Spectral Templates for AGNs and Galaxies , 2009, 1004.5415.

[17]  A. Kinney,et al.  Template ultraviolet to near-infrared spectra of star-forming galaxies and their application to K-corrections , 1996 .

[18]  Huan Lin,et al.  Estimating the redshift distribution of photometric galaxy samples , 2008 .

[19]  R. J. Brunner,et al.  TPZ: photometric redshift PDFs and ancillary information by using prediction trees and random forests , 2013, 1303.7269.

[20]  Robert J. Brunner,et al.  SOMz: photometric redshift PDFs with self organizing maps and random atlas , 2013, ArXiv.

[21]  Harland W. Epps,et al.  THE KECK LOW-RESOLUTION IMAGING SPECTROMETER , 1995 .

[22]  B. Garilli,et al.  Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey , 2006, astro-ph/0603217.

[23]  James E. Geach,et al.  Unsupervised self-organized mapping: a versatile empirical tool for object selection, classification and redshift estimation in large surveys , 2011, 1110.0005.

[24]  Pedro M. Domingos,et al.  On the Optimality of the Simple Bayesian Classifier under Zero-One Loss , 1997, Machine Learning.

[25]  N. Benı́tez.  Bayesian Photometric Redshift Estimation , 1998, astro-ph/9811189.

[26]  G. Zamorani,et al.  The Zurich Extragalactic Bayesian Redshift Analyzer and its first application: COSMOS , 2006 .

[27]  Scott Croom,et al.  The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations , 2011, 1108.2635.

[28]  M. J. Way,et al.  Can Self-Organizing Maps Accurately Predict Photometric Redshifts? , 2012 .

[29]  Anthony H. Gonzalez,et al.  LOW-RESOLUTION SPECTRAL TEMPLATES FOR ACTIVE GALACTIC NUCLEI AND GALAXIES FROM 0.03 TO 30 μm , 2010 .

[30]  Leonard E. Trigg,et al.  Technical Note: Naive Bayes for Regression , 2000, Machine Learning.

[31]  J. Newman,et al.  EXTENDED PHOTOMETRY FOR THE DEEP2 GALAXY REDSHIFT SURVEY: A TESTBED FOR PHOTOMETRIC REDSHIFT EXPERIMENTS , 2012, 1210.2405.

[32]  E. al.,et al.  The Sloan Digital Sky Survey: Technical summary , 2000, astro-ph/0006396.

[33]  A. Szalay,et al.  Slicing Through Multicolor Space: Galaxy Redshifts from Broadband Photometry , 1995, astro-ph/9508100.

[34]  K. Gorski,et al.  HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , 2004, astro-ph/0409513.

[35]  Ofer Lahav,et al.  ANNz: Estimating Photometric Redshifts Using Artificial Neural Networks , 2004 .

[36]  SLAC,et al.  Sample variance in photometric redshift calibration: cosmological biases and survey requirements , 2011, 1109.5691.

[37]  L. M. Sarro,et al.  Automated supervised classification of variable stars - I. Methodology , 2007, 0711.0703.

[38]  A. Connolly,et al.  THE DEEP2 GALAXY REDSHIFT SURVEY: DESIGN, OBSERVATIONS, DATA REDUCTION, AND REDSHIFTS , 2012, 1203.3192.

[39]  S. Gwyn,et al.  THE CANADA–FRANCE–HAWAII TELESCOPE LEGACY SURVEY: STACKED IMAGES AND CATALOGS , 2012 .

[40]  S. J. Lilly,et al.  Precision photometric redshift calibration for galaxy–galaxy weak lensing , 2007, 0709.1692.

[41]  Alexander S. Szalay,et al.  Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample , 2009, 0907.1660.

[42]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[43]  D. Schlegel,et al.  Maps of Dust IR Emission for Use in Estimation of Reddening and CMBR Foregrounds , 1997, astro-ph/9710327.

[44]  W. M. Wood-Vasey,et al.  THE BARYON OSCILLATION SPECTROSCOPIC SURVEY OF SDSS-III , 2012, 1208.0022.

[45]  Alexander S. Szalay,et al.  Toward More Precise Photometric Redshifts: Calibration via CCD Photometry , 1997, astro-ph/9703058.

[46]  David W. Hogg,et al.  STAR–GALAXY CLASSIFICATION IN MULTI-BAND OPTICAL IMAGING , 2012, 1206.4306.

[47]  Lior Rokach,et al.  Ensemble-based classifiers , 2010, Artificial Intelligence Review.

[48]  R. Trotta.  Applications of Bayesian model selection to cosmological parameters , 2005, astro-ph/0504022.

[49]  Robert J. Brunner,et al.  Robust Machine Learning Applied to Astronomical Data Sets. III. Probabilistic Photometric Redshifts for Galaxies and Quasars in the SDSS and GALEX , 2008, 0804.3413.

[50]  Teuvo Kohonen,et al.  The self-organizing map , 1990 .

[51]  Manda Banerji,et al.  A comparison of six photometric redshift methods applied to 1.5 million luminous red galaxies , 2008, 0812.3831.

[52]  D. Weedman,et al.  Colors and magnitudes predicted for high redshift galaxies , 1980 .

[53]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[54]  S. Baumont,et al.  A new method to improve photometric redshift reconstruction - Applications to the Large Synoptic Survey Telescope , 2013, 1301.3010.

[55]  R. Nichol,et al.  The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological constraints from the full shape of the clustering wedges , 2013, 1303.4396.

[56]  D. Schlegel,et al.  Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds , 1998 .