Photometric Redshifts for Public Data Release 1
The Photo-z Working GroupFebruary 17, 2017

1Overview

J. Coupon, B.C. Hsieh, S. Mineo, A. Nishizawa, J. Speagle, and M. Tanaka participate in
the photo-z production run and independently compute photo-z’s. Our catalog products areavailable from the database and PDFs from the photo-z release page on the data release site.
• Please carefully read the data release paper first. Problems in the photometry
propagates to photo-z’s.
• We have defined a set of common outputs from our codes (see Section 3). We
also (mostly) homogenized the format of our P(z) files.
• We have two new quantities in the common outputs: ’best’ point estimate
and photo-z ’risk’ (see brief note in Section 3 and photo-z release paper (inprep) for more details). photoz best is likely better than the commonly used
median estimates and photoz risk is also better indicate of photo-z reliability
than photoz conf.

2

Catalog construction and how the photo-z’s are computed
1. JS collected spectroscopic, grism, and high accuracy photometric redshifts from the literature and cross-matched with HSC objects. He then computed weights to reproduce
multi-color-magnitude distributions of the target galaxies from the Wide layer. Refer toAppendix for details of this procedure.
2. The catalog is used for training/validation/test. JS performs cross-validation to train andvalidate his model. The other people use the hold-out validation technique using 4/5 ofthe sample. The remaining 1/5 is not used for training and validation. It is used for test.
3. A set of QA plots on are generated using photo-z’s for the test sample (not currently
available on the photo-z release page). The training sample is matched to the COSMOS
wide-depth best/median/worst data and photo-z’s are run on these catalogs as well andQA plots to evaluate the seeing dependence are generated. The median seeing stack isused for the plots available from the data release site.
4. Once the calibrations are done, the photo-z codes are run on the full UD, D, and Widecatalogs prepared by AN. The photo-z’s and other products are ingested into the databaseand made available to the users.

3Photo-z products

Our products are not limited to photo-z, but some codes deliver ancillary information such as
stellar mass, rest-frame magnitudes, etc. For the available products in this release, please referto the schema browser. We are aware that some hardcore users would like to use the full P (z)information. Full P (z) tables is available at the photo-z release page.
In this release, the photo-z team defined a set of common outputs for all the codes:• ID : object ID. This should be used to join tables.
∫• several photo-z
point estimates: zmean = zP (z)dz, zmode is mode of P(z), zmedian is∫ zmediandefined as z=0P (z)dz = 0.5, zmc is a Monte-Carlo draw from P (z). zbest is a newpoint estimate and is defined as a optimal estimate to minimize a loss function in theform:
1loss(z, ztrue ) = 1 −,(1)2
1 + ( ∆zσ )truewhere ∆z = z−z1+ztrue and σ = 0.15. For further details, please refer to the photo-z releasepage.

• photo-z confidence intervals: zlow95 is defined aszhi95 are defined in a similar manner.
• photo-z rms around each point estimate:mate.

√∫• Redshift confidence for each point estimate:∫ zlow95
z=0P (z)dz = 0.025. zlow68 , zhi68 , andP (z)(z − zpt )2 dz, where zpt is a point esti-∫ zpt +0.03(1+zpt )zpt −0.03(1+zpt ) P (z)dz• photo-z risk, which can be used to identify likely bad photo-z objects. It is defined as theintegrated probability of P(z) convolved with the loss function.

4Statistics

A set of plots to characterize the photo-z accuracy is provided for each code on the data releasesite. Before you look at these plots, please be aware of the following important points/caveats.
1. In all the plots, we consider objects down to icmodel = 25. We impose this cut
because the ’true’ redshifts at faint mags are mostly from COSMOS 30-band photo-z’s
and they are not reliable for very faint objects.
2. We assume that the high accuracy photo-z’s based on the 30-band photometry, which
comprise a large fraction of our sample, are the truth table and we compare our 5-bandphoto-z’s against them. However, some of the 30-band photo-z’s will be incorrect and theabsolute numbers here should be taken with caution.
3. We used to include stars in the statistics, but they are not included this time.
4. No object clipping is applied. However, some users may want to apply clipping in orderto reduce outliers. Redshift risk is a useful indicator of the reliability of a photo-z.
We use the ’standard’ metrics to characterize photo-z accuracy; bias, dispersion, and outlierrate. The definitions adopted in the literature are not always the same and we explicitly definethem here. In what follows, we denote the true redshifts as zref .
• Bias: Photo-z’s may systematically be oﬀ from spectroscopic redshifts and we call thissystematic oﬀset bias. We compute a systematic bias in (zphot − zspec )/(1 + zspec ) byapplying the biweight statistics (Beers et al. 1990). We iteratively apply 3σ clipping for 3
times to reduce outliers.

• Dispersion: In the literature, dispersion is often computed as(zphot − zspecσconv = 1.48 × MAD
1 + zspec),(2)

where MAD is the median absolute deviation. Note that this definition does not accountfor the systematic bias. In addition to this conventional definition, we also measure thedispersion by accounting for the bias using the biweight statistics. We iteratively apply a3σ clipping as done for bias to measure the dispersion around the central value. We denotethe conventional dispersion and the biweight dispersion as σconv and σ, respectively.
• Outlier rate: The conventional definition is(Nfoutlier,conv =)|zphot −zspec |> 0.15
1+zspec

Ntotal,(3)

where outliers are defined as |zphot − zspec |/(1 + zspec ) > 0.15. Again, this definition does
not account for the systematic bias. The threshold of 0.15 is an arbitrary value but isprobably fine for photo-z’s with several bands. It is clearly too large for those with manybands. Together with this conventional one, we also define outliers as those 2σ away fromthe central value (these σ and center are from biweight; see above). This 2σ is an arbitrarychoice, but it is motivated to match reasonably well with the conventional one for several
band photo-z’s. We will denote the σ-based outlier fraction as foutlier and the conventional
one as foutlier,conv .
In addition to these standard metrics, we include the loss defined in Section 3.

Now, we explain each plot –page A1: The HSC 5-band photo-z plotted against zref (they are actually high accuracy
spec/grism/photometric redshifts from various surveys). A set of basic statistics has been computed and are shown in the plot. The solid line is zphot = zref and the dashed lines arezphot = zref + 0.15(1 + zref ). Objects outside of the dashed lines are regarded as outliers in theconventional definition (foutlier,conv ).
page A2: Dispersion and outlier rate (both conventional ones), and loss plotted against i-band
magnitude. It should be straightforward to read this figure.
page A3: Bias, dispersion, and outlier rate computed with the biweight method are plottedagainst i-band magnitude. The horizontal dashed lines show ±0.01 and they might be useful toread the amount of bias oﬀ the figure.
page A4: Conventional dispersion and outlier rate, and loss plotted against redshift.
page A5: Same as page A4, but for bias, dispersion, and outlier rate with biweight. The horizontal dashed lines show ±0.01.

page A6: Fraction of objects that are consistent with zref within the 68% (red) and 95% (blue)
intervals. This plot shows the accuracy of photo-z uncertainties. If the uncertainties are correctly estimated, the fractions should be 68% and 95%.
page A7-A9: Redshift distribution of the photo-z selected objects. The panels are for diﬀerent
redshift bins. On the right of each panel, mean photo-z, mean of the true redshifts, and fractionsof foreground and background objects are shown. Note that the mean is straight mean and isstrongly aﬀected by outliers.

A: training sample construction by J. Speagle
Catalog quantities:• Identifiers for each object include ID, (ra,dec), and (tract,patch) coordinates.
• Fluxes include psf fluxes, cmodel fluxes, cmodel exp fluxes, and cmodel dev fluxes. In
addition, I’ve included 1.5-arcsec aperture photometry with target PSF=1.1 arcsec takenfrom the afterburner run, with associated uncertainties taken from 1.5-arcsec aperture
photometry without PSF matching.
• Shapes are measured using the sdss shape parameters.
• Merge measurement flags, attenuation data, and extendedness are also included.
• Redshift and 1-sigma error.
• Parent survey, where: SDSS=1, DEEP2/DEEP3=2, PRIMUS-3, VIPERS=4, VVDS=5,GAMA=6, WIGGLEZ=7, COSMOS=8, UDSZ=9, 3DHST=10, FMOS-COSMOS=11• Redshift type: spec-z=1, grism/prism-z=2, photo-z=3.
• Depth: udeep=1, deep=2, wide=3• Emulated errors, which are indicated by the ” wide” suﬃx.
• k=5 shuﬄed cross-validation folds, which are labeled in the ’crossval sample’ field.
• Color/mag weights (’crossval weights’) to forecast performance to a generic wide-selected
sample. (These might be zero.)
Database selection criteria:
Photometry for the parent catalogs was selected from the database using the following cuts:• detect is primary• NOT [grizy]centroid sdss flags• NOT [grizy]cmodel flux lags
• NOT [grizy]flags pixel edge
• NOT [grizy]flags pixel interpolated center• NOT [grizy]flags pixel saturated center• NOT [grizy]flags pixel cr center• NOT [grizy]flags pixel bad
Spec-z quality requirements:
I include objects according to the following criteria:
Public spec-z/prism-z data:• z>0.01 (confirm star removal) and z<9 (no quasars)• sigma z<0.005(1+z)• SDSS/BOSS: zWarning=0 (no apparent issues), z<1.2• DEEP2: qFlag=3-4 (>95% confidence)• PRIMUS: qFlag=4 (highest quality)• VIPERS: qFlag=3-4 (>95% confidence)• VVDS: qFlag=3-4 (>95% confidence)• GAMA: qFlag>=4 (very confident)• WIGGLEZ: qFlag>=4 (very confident)• UDSZ: qFlag=all (provisional catalog only includes >95% confidence redshifts)• FMOS-COSMOS: qFlag=3-4 (>95% confidence), z>0.01, flag star=False.
3DHST data:• Flag star=False• 0<z<9 (no stars, quasars, or failed redshifts)• For grism-zs/photo-zs:
sigma z68<0.05(1+z), sigma z68=max(zh68zmed,zmed-zl68)
sigma z95<0.1(1+z), sigma z95=max(zh95zmed,zmed-zl68)
COSMOS data:
Spec-z:• 3 <= qFlag < 6 (>99% confidence redshifts)• 0 < z < 9.9• For objects with repeat observations, sigma z<0.005(1+<z>)
photo-z:• No bad photometry (flag capak)• Type=0 (galaxies only)• chi2(gal)<chi2(star), chi2 reduced(gal)<5 (reasonable fits)• No secondary peaks (z secondary)• Mstar>7.5 (stellar mass successful)• 0<z<9 (no stars, quasars, or failed redshifts)• sigma z<0.05(1+z), sigma z=max(zh68-zmed,zmed-zl68)
I find this selects a set of spec-z’s that do not diﬀer substantially from those selected Masayuki’s”homogeneous” quality flags.
Photometry Quality Cuts:
I have limited the catalog to only include objects with (all) fluxes properly measured in all 5bands. This removes ∼ 1% (∼4000 objects) from the parent sample, mostly from failed measurements in the afterburner photometry. I have confirmed this cut is (to first order) unbiased incolor/mag and redshift. Note that this means I include objects with poorly measured/undefined
shapes. I found that cut removed a much larger (∼7%) portion of the sample, and substantiallybiased the sample at higher redshifts.
Cross-Matching Procedure:
All spec/grism/prism/photo-z data are (uniquely) matched successively to the udeep>deep>wide
data to within 1” (the closest object is selected if duplicate matches occur), where I’ve supplemented the objects matched in the database with 3DHST/COSMOS high quality photo-z’s andprivate COSMOS spec-z’s. Note that the DEEP3 redshifts are not included in this version due
to some technical issues. I hope to include them in future releases.
Error Emulation:
Since objects in the catalog are from a variety of depths, I emulate wide-depth photometricerrors by matching photometric noise-to-signal ratio (N/S) to a target dataset of ∼500k objects
from the wide field (selected with the same database selection criteria) using k-d trees. I findthat just selecting the closest neighbor in 5-band flux space (per flux type) or 3-parameter shapespace (per band) reproduces the general distribution (both mean error and variance among S/Nmeasured for similar 5-band SEDs) quite well.
Color/Mag Weights:
Finally, I’ve included a series of color/mag weights under that should be used to ensure appropriate weighting when forecasting results to the wide data. I computed these using an improvementof the kNN approach used in, e.g., SDSS, where I’ve actually gone through the trouble to compute numerical approximations to the Bayesian evidence among a group of ∼100 ”neighbors”
in color/mag space (selected across multiple Monte Carlo runs). I’ve confirmed this successfully
matches across basic magnitude/color distributions.