1. Photometric Redshifts with Poisson-only Noise Christian Wolf Oxford Physics Edinburgh - 6 May 2009

2. Talk Outline I.Why Photo-z’s? II.State of the Art III.Future challenges IV.The  2 -empirical approach V.Persistent photo-z issues  2 -test: noisy model VII.The PHAISE proposal

3. I. Why Photo-z’s?  z < 0.01 Stebbins & Whitford, AJ, 1948 Photography is deeper than spectroscopy! Baum 1957

4. Baum 1962, IAU Symp. 15

5. Photo-Zeeing in the 80’s/90’s Koo 1985 –  z /(1+z) ~ 0.04 @ z < 0.6 –UBVI photographic plates Loh & Spillar 1986 –Degrading all filter images to worst seeing important –Star and galaxy library –10% outliers Half z phot wrong –Insufficiently blue templates –Photometric blends Half z spec wrong –Blends –Single-line detections Connolly et al. 1995 –4-D space (z,U-B,B-R,R-I) Distribution has D f = 1.8 –Colour ‘plane’ at z = [0,0.4] rotation after one filter –Step-wise quadratic fits –  z /(1+z) < 0.04 @ z < 0.8

6. Redshift Errors & Resolution Objects at different redshifts Filterset 's fixed z = 0.843 z = 1.958 z = 2.828 400 nm 1000 nm flux / qef G2 star vs. QSO z=3

7. II. State of the Art: Medium-band SEDs rms 0.008 7%-20% outliers rms 0.008 (R<21) 1 outlier QSOs at z~2.8 R=23.8R=22.9R=21.5 R=20R=22 R=23.7 Galaxies at z~0.45

8. State of the Art: ugriz-only Collister & Lahav 2004 ANN  2 template ~4% outliers  z/(1+z)>0.1 rms  z/(1+z) = 0.042 Bias -0.017 ~0% outliers  z/(1+z)>0.1 rms  z/(1+z) = 0.023 Bias ~0.00 ANN easy at z<1: no ambiguities… but wait for future data!

9. III. Future Challenges Catastrophic failures & misclassifications Large z errors Mean z bias Unrealistic z errors

10. Origin of Challenges Catastrophic failures & misclassifications Large z errors Mean z bias Unrealistic z errors Model ambiguities in colour space PDF too unconstrained PDF wrong Mismatch between data and model

11. Common Fixes Catastrophic failures & misclassifications Large z errors Mean z bias Unrealistic z errors Model ambiguities in colour space PDF too unconstrained PDF wrong Mismatch between data and model Add priorsAdd more dataRepair models Use template error function

12. Why do These Matter? Super-large photo-z surveys for cosmology –Now: PanStarrs, DES –2015++: LSST, IDEM Redshift bias from –Model:data calibration –Catastrophic outliers |  z| ≈ |  z outlier |   outlier Kitching, Taylor & Heavens: –  w ≈ 5  z (3D cosmic shear) –  z = 0.01 unacceptable  1% outliers unacceptable Even spectroscopic surveys –May have 1% wrong z’s –Have incompleteness, i.e. more undiscovered outliers

13. http://www.astro.uni-bonn.de/~hendrik/PHAT/index.html

14. Back to The Principles: Overview Farb- bibliothek Schätzer/ Klassifikator result model data estimator spectral energy distribution PDF: p(z) empirical data or external template  2 -fitting artificial neural net learning algorithms

15. Back to The Principles: Overview Farb- bibliothek Schätzer/ Klassifikator result model data estimator spectral energy distribution PDF: p(z) empirical data or external template  2 -fitting artificial neural net learning algorithms Frequentist precision statistics: = “Using what IS there: N(z)!” Bayesian frontier exploration: = “What do we (not) know: p(z)=?”

16. Model-Estimator Combinations Code  2 NN Model Template  Empirical   2 +PDF  Ambiguity warning NN –No PDF, no warning Template model +Can be extrapolated in z,mag –Calibration issues –Priors’ issues Empirical model +Good priors +No calibration issues –Can not be extrapolated

17. Model-Estimator Combinations Code  2 NN Model Template  Empirical   2 +PDF  Ambiguity warning NN –No PDF, no warning Template model +Can be extrapolated in z,mag –Calibration issues –Priors’ issues Empirical model +Good priors +No calibration issues –Can not be extrapolated ?

18. VI. The  2 -empirical Approach Goal –Combine  2 -PDF with reliability of empirical model Suggest –Replace templates with empirical model: has correct calibration & priors, but has also noise However –PDF from  2 -model testing only correct, if model correct and noise-free –Templates are noise-free but incorrect, so produce wrong PDF as well

19. Compare: Kernel Regression From global fits (1980s) to local fits (2000s) –Locally optimal solution –Requires more data and computing power Kernel function –Smooth over wide range for robust solution –Smooth over small range for good representation Identical to  2 -fitting if –Model noise-free –Gaussian kernel function with  =  data Colour given: Locally fit z(colour) z

20. Equations:  2 -testing Probability of single given model object to produce data object Parameter estimate Expected error Bimodality detection p z

21. For Now: Ignore Model Errors SDSS QSO sample –Plenty of z-ambiguities –DR5: 75,770 objects split half:half into model:data –Pretend noise-free model Richards et al. 2007

22. Result: Non-bimodal Objects Fraction of outliers with |  z| > 3  z,limit Photo-z “bias” = mean  z of non-outliers (non-outliers) Fraction of sample with  z <  z,limit

23. Results: Non-bimodal Objects Fraction of outliers with |  z| > 3  z,limit Photo-z “bias” = mean  z of non-outliers (non-outliers) Fraction of sample with  z <  z,limit  z rms   z

24. Result: Bimodal Objects 15474 detected ambiguities –Two z’s given one colour –Need more data to break Meanwhile –Trust more probable z Mean p-ratio 78:22 predicts 12077 right : 3397 wrong 12051 right indeed! –Use two weighted results Reliable: p high ≈ f high Sensitivity limits? 8% 1:>20 and 1% 1:>50 Undetected ambiguities inevitable (= erroneously uni-modal) – 30% of space, undetected 1:50-ambiguity  0.6% outliers

25. Result: Redshift Distributions Histogram of  z phot  -estimates count bimodal objects twice using p-weights Co-addition of all p(z)  p(z) inform beyond  z phot 

26. Result: Size of Model Sample

27. V. Persistent Photo-Z Issues 1.RMS redshift error Has a floor supported by intrinsic scatter, deeper photometry useless 2.Redshift bias Sub-samples can show local bias even when method globally bias-free 3.Catastrophic outliers Faint ambiguities (extreme p-ratio) undetectable, only guard is all-out spectroscopy

28. Error Floor from Intrinsic Scatter Example: –QSO near (g-r)~1 or z~3.7 –z signal: Ly forest in g-band Training sample in box –Redshift distribution: mean 3.66, rms 0.115 –RMS/(1+z) = 0.024 Testing sample in box –RMS/(1+z) error 0.023 Locally linear

29. Local Redshift Biases

30. Not an issue when plotted over z phot (by design!)

31. Outliers from Undetected Ambiguities Model objects within kernel: N primary + N 2nd = N model,local Assume  2nd > 0; observe N 2nd = 0:  N 2nd  = 1 Hence, individual residual outlier risk:p 2nd = 1/N model,local

32. Incomplete Models Mean Outliers Incomplete targeting –No problem, use weights Incomplete z recovery –Model completeness f(z) –Main reason: z different –Missed “model outliers” –Part of data PDF missing Maximum bias risk for objects at fixed colour

33. Incomplete Models Mean Outliers Incomplete targeting –No problem, use weights Incomplete z recovery –Model completeness f(z) –Main reason: z different –Missed “model outliers” –Part of data PDF missing Maximum bias risk for objects at fixed colour Assume deep survey –  non-recov =0.2 –|  z out |=1  |   z  |=0.2 !!! Spectroscopic incompleteness deserves by far the greatest concern in empirical redshift estimation.* * |  z  |<10 -3 means 99.9% completeness & reliability

34. Model  q1q1 q2q2 q1q1 q2q2  2 -Test: Noise-free Model p(data|model) =  model  G  2 (data) G data = G  2   data =    2

35. Model  q1q1 q2q2 q1q1 q2q2 q1q1 q2q2 q1q1 q2q2 VI.  2 -Test: Noisy Model p(data|model) =  model  G  2 (data) G data = G  2   data =    2 G data = G model  G  2   data =   model +    2    2 =   data -   model

36. Data Noise vs. Model Noise If   data >   model –Replace model point by Gaussian    2 =   data -   model If   data ≈   model –When    2  0 then also N model,local  0 and outlier risk  1 –Define p(z) only for regions larger than one object or… If   data <   model –Larger target smoothing i.e. Resample data point with   resample =   target -   data Replace model point by Gaussian    2 =   target -   model

37. Error Propagation: Equations Locally linear Model has scatter Data has scatter At fixed colour: z phot =  z  True z scatter: Estimated photo-z error: Only equal if

38. Noisy Model, Noisy Data: n(z)=? Use noise levels of  data = 0.1414  model = 0.1000 Reconstruction of n(z) with Poisson precision

39. Revisiting The  data ~  model Case  z rms   z   2  0

40. Unifying  2 -testing with Kernel Regression - Practical Requirements Merge two approaches –Model smoothing by kernel function –Correct  2 error scale Strictly require –Target smoothing scale constant across space –Data error > model error Either from the start Or noise be introduced into data on purpose Desire for –Better model photometry –Constant data error scale Bright objects: errors in magnitudes Faint objects: errors in flux units (background) Or transform mag scale so that error constant Issues –Varying exposure depth or interstellar extinction

41. VII. The PHAISE Proposal PHoto-z Archive for Imaging Survey Exploitation –Gaussian-precision photo-z code & residual risk quantification from model incompleteness/size moves all attention to model –Residual outlier risk   incomplete –Noise floor on n(z)  2 n(z)  1/N model,z-bin The plan: A central repository for empirical model data –Avoid duplication of efforts, provide “the best empirical model” –Best-possible n(z)/photo-z quality from here, by definition –Dynamic and growing with time, well-known incompleteness –Web submission of small “photo-zeeing” jobs or customer installation for large applications (PanStarrs, LSST, …)

42. PHAISE Issues & Plan Calibrating new photo-z survey to PHAISE? –Pure calculation of colour transformations reliable? –Must observe calibration fields? Digesting diverse input –Start with SDSS, VVDS, GOODS etc. –Keeping track of sources of incompleteness 5-year goal: It works! –Existing spectroscopic sources digested –Incompleteness at R>22 too high for cosmology 10-year goal –Deep complete spec-z survey fills gaps –VIMOS, FMOS, SIDE,… –“Fundamental” limits, e.g. source blending, AGN...

43. Summary I.Presented method delivers n(z|c) or photo-z with Poisson precision if model complete II.Completeness of empirical spectroscopic model in faint regime is primary quality limit III.Need deep, large, very complete spec survey! IV.Combine resources, do it once, and ABAP Set up PHAISE, codes, technicalities Propose “The Deep Complete” survey Campaign for suitable optical + NIR instrumentation