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On the cosmological performance of photometrically classified supernovae with machine learning

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Using simulated photometric supernovae, this paper shows that machine-learning classification with per-redshift purity thresholds chosen by a bias-variance tradeoff can keep roughly 75% of the type-Ia distance information and recover the…

desk verdict Useful benchmark for photometric SN classification, but the headline 75%/33% information-retention numbers are selected using the test set's true distance moduli, so treat them as best-case in-sample results. read the letter →

arxiv 1908.04210 v3 pith:WXGQWKFO submitted 2019-08-12 astro-ph.CO astro-ph.IM

Marcelo Vargas dos Santos , Miguel Quartin , Ribamar R. R. Reis This is my paper · ORCID
classification astro-ph.COastro-ph.IM
keywords supernovaclassificationphotometricsupernovaemachinelearningbias-variancetradeoffeffectivecompletenesscosmologicalconstraintsSALT2SNPCC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks how much cosmological information survives when supernova types are assigned by machine-learning classifiers instead of spectroscopy, since upcoming surveys will observe far more supernovae than they can confirm spectroscopically. Using the simulated SNPCC light-curve catalog, it shows that if one chooses the classification threshold in each redshift bin by minimizing the mean squared error of the distance modulus, the resulting photometrically classified catalogs recover the fiducial cosmology within half a sigma. With SALT2 light-curve features the catalogs retain about 75% of the type-Ia distance information, and with Newling-model or wavelet features about 33%. The result matters because it quantifies how much dark-energy constraining power remains in a purely photometric sample.

What carries the argument

The machinery is the bias-variance decomposition of the distance-modulus error, MSE = Var[Delta_mu] + $b^{2}$, applied to the choice of classification threshold. A threshold maps to a catalog purity; raising purity usually lowers contamination bias but raises variance as the catalog shrinks, so the paper selects the purity in each redshift bin that minimizes the total MSE rather than maximizing purity alone. The other load-bearing object is the effective completeness, C_eff = (sigma_Ia / $\sigma$)^2, which converts the ratio of parameter errors between a perfect and a photometric classifier into an effective number of type-Ia supernovae; this is the quantity behind the 75% and 33% information-retention numbers.

What would settle it

Re-run the pipeline on the same simulated catalog but with the test set split into a threshold-tuning portion and a held-out portion: choose the per-bin purities from the tuning portion only, then measure cosmology on the held-out portion; if the effective completeness falls well below 75% or the recovered parameters shift by more than half a sigma, the claimed transfer to real surveys fails.

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Extended reading notes

Core claim

The central claim is that a machine-learning-selected supernova catalog is cosmologically usable without spectroscopic confirmation. In the paper's implementation, each light curve receives a probability of being type Ia; raising the probability threshold raises catalog purity but discards objects and, surprisingly, can increase rather than decrease distance bias because the contaminants are not symmetric in absolute magnitude. The paper therefore proposes choosing, separately in each redshift bin, the purity threshold that minimizes the total MSE (variance plus squared bias) of the SALT2 distance modulus. With this binned-purity selection, all feature sets recover the fiducial Omega_m0 and w within half a sigma, and the effective completeness reaches about 75% for SALT2 features, 30-35% for Newling and wavelet features, and about 20% for Karpenka features.

Load-bearing premise

The result assumes that purity thresholds chosen using the true distances of the same simulated test catalogs will transfer to real surveys where those distances are unknown, and that the per-bin absolute-magnitude calibration applied beforehand does not erase the very bias being measured.

Editorial extensions

If this is right

  • If the claim holds, spectroscopic follow-up is not a prerequisite for competitive dark-energy constraints: a purely photometric catalog can carry most of the type-Ia distance information.
  • SALT2-style features are worth the extra fitting cost, since they preserve roughly twice as much information as parametric or wavelet alternatives.
  • Threshold choice should be treated as a statistical decision, not a fixed purity cut; optimizing per redshift bin keeps biases below 0.03 mag in the range 0.4 < z < 1.1.
  • The sign change of the classification bias at high purity means that pushing purity upward can hurt cosmology; MSE-based selection protects against that.
  • Even in the pessimistic case that SALT2's advantage is partly an artifact of the simulation, the other feature sets still retain about a third of the information, so photometric classification remains viable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same pipeline were run on a data set where the purity thresholds are tuned only on a training subset and then frozen before any cosmology is measured, the 75% figure would likely drop; the paper tunes thresholds on the true distances of the same test catalogs, so the headline number should be read as an upper bound.
  • The fact that high-purity samples are dominated by type-Ibc contaminants similar in magnitude to type Ia suggests a natural extension: instead of hard cuts, feed the classifier's continuous probabilities into a Bayesian sample-combination estimator, which could recover some of the lost information.
  • The effective-completeness ratio could serve as a standardized figure of merit for comparing photometric classifiers across surveys, since it is directly tied to cosmological parameter errors rather than to AUC scores.
  • Because SALT2 was among the models used to generate the simulated SNeIa, a fair test would rerun the comparison on simulations built from independent explosion models; the true retention may sit closer to the 33% figure of the other feature sets.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. Using the SNPCC simulated supernova catalog, the authors train supervised classifiers (AdaBoost, Random Forest, Extra-Trees, Gradient Boost, XGBoost, and TPOT) on four feature sets (SALT2 light-curve fits, Newling, Karpenka, and wavelet coefficients), with and without host-galaxy photometric redshift. They compare AUC and Average Precision scores and then perform cosmological fits of Omega_m0 and w on catalogs selected by purity thresholds. They propose a 'binned purity' selection that minimizes the RMSE of distance moduli in each redshift bin. They report that the best ML catalog with SALT2 features retains roughly 75% of the cosmological information of a perfect SNeIa classifier, while Newling and wavelet features retain around 33%, and that all fitted parameters agree within half a sigma of the fiducial model. The best TPOT pipelines are provided in Appendix B.

Significance. If the 75%/33% information-retention figures and the half-sigma agreement describe expected out-of-sample performance, this would be a useful guide for photometric SN surveys such as LSST. The paper's strengths include a systematic comparison of many classifiers and feature sets on a public benchmark, a clear presentation of the bias-variance tradeoff, and explicit reproducible pipelines in Appendix B. However, as detailed in the major comments, the headline numbers are obtained through in-sample optimization on the same test catalogs used to report the final constraints, so they are best interpreted as upper bounds rather than validated on-sky performance. The qualitative ranking of feature sets is likely robust, but the specific percentages in the abstract should not be taken as expected real-survey performance.

major comments (3)
  1. [Sec. 5.2, Eq. (7), Eq. (15), Table 6] The binned-purity threshold is chosen by minimizing the RMSE defined in Eq. (7), with Delta-mu computed from the true simulated distance modulus and the fiducial model, on the same test catalogs that are then used for the cosmological fits (Eq. 15) and for the effective completeness in Table 6 (Eq. 17). This is an oracle selection that requires knowing the true SNeIa types and true distances of the objects whose purity is being optimized. Consequently, the headline results - roughly 75% (SALT2) and 33% (Newling/wavelets) information retention and the 'within half a sigma' agreement - are in-sample, best-case numbers, not expected performance for a real photometric survey. Please demonstrate the selection method on a validation set that is not used for the final constraint (for instance, split the 20,219 test light curves into a threshold-optimization set and a separate cosmology set), or explicitly state in the abstract and conclusions that these figures are upper bounds assuming perfect knowledge of the test truth.
  2. [Appendix A] The MB(z) calibration uses the pure SNeIa catalog to measure and subtract, per redshift bin, the mean offset between the SALT2 distance moduli and the fiducial mu(z). This removes light-curve fitting bias by construction, and the statement in Appendix A that this procedure 'guarantees that any cosmological bias in the classified catalogs would be a result of the ML classification code' overstates what is shown: the correction also absorbs any distance-estimator bias common to the perfect-classifier and ML catalogs, and it is derived using the true class labels. Please clarify that the comparison is conditional on perfect distance calibration, and discuss whether a per-bin MB(z) correction computed from the pure SNeIa catalog could itself remove part of the classifier-induced bias if the contamination varies with redshift.
  3. [Sec. 6, Conclusions] The paper appropriately notes that the Bias-Variance tradeoff assumes the bias cannot be modeled. However, this caveat does not address the fact that the per-bin purity thresholds themselves are selected using the true Delta-mu of the test set. Please add a discussion of how the thresholds would be chosen in practice (for example, using a spectroscopically confirmed subset as a validation set) and state how the reported information retention would change if the thresholds were fixed a priori rather than optimized on the same test catalogs.
minor comments (5)
  1. [Abstract] The sentence 'such as the The Rubin Observatory Legacy Survey of Space and Time' contains a duplicated 'the'; please correct.
  2. [Fig. 3] The vertical axis label 'Regression Scores' is unclear; consider labeling it 'RMSE components' or define the plotted quantities more explicitly in the caption.
  3. [Eq. (16)] The notation C_{ij} is used both for the ensemble-averaged covariance and for a single-catalog quantity Delta-mu_i Delta-mu_j; please clarify the averaging being performed.
  4. [Table 5] The reference 'Möller & Deboissì Ere (2018)' contains a typo; the correct name appears to be 'de Boissière' and the reference entry should be checked for accuracy.
  5. [Sec. 5.2] The text uses RMSE and MSE interchangeably; since Eq. (7) defines both, please state explicitly which quantity is minimized in the binned-purity selection.

Circularity Check

1 steps flagged · score 6.0 of 10

The headline 75%/33% information retention is an in-sample oracle result: per-redshift-bin purity thresholds are chosen by minimizing the RMSE on the same test catalogs that later produce the quoted cosmological constraints and effective completeness.

  1. fitted input called prediction [Section 5.2 (threshold selection), Eqs. (15)-(17), Table 6, abstract]
    "We thus understand that the best way of selecting the sample is to choose the purity values in each redshift bin that minimize the RMSE, which we dub binned purity. ... Defining the error as σ 2 i = MSEi =⟨∆ ¯µ2 i⟩, where as before ∆ ¯µ≡ ¯µ− ¯µ f id(zsim), we generalize it for correlated bins as Ci j =⟨∆ ¯µi∆ ¯µ j⟩ so the covariance for a single catalog is Ci j = ∆ ¯µi∆ ¯µ j, therefore Ci j = (Vari/Ni_SN) δi j + bib j . (16)"

    The binned-purity thresholds are selection hyperparameters chosen by minimizing the RMSE, and the RMSE is computed from ∆µ = µ − µ_fid(zsim), i.e., from the true simulated distance moduli of the same test catalogs. The later cosmological analysis uses Eq. (15) with a covariance (Eq. 16) built from exactly those same ∆µ residuals, and the reported effective completeness (Eq. 17) is derived from the width of that fit. The 75%/33% figures are therefore the value of the (closely related) objective after optimizing it on the test set, not an independent out-of-sample prediction. A real survey has no µ_fid, so the selection rule cannot be applied as described without ground truth; the abstract's performance claim is an in-sample, oracle-optimized number.

full rationale

The classifier training itself is not circular: the ML models are trained on 1100 SNe with 5-fold cross-validation and tested on a separate 20219-SN set, and the AUC/AP comparisons are honest measurements. The circularity is confined to the final cosmological-performance claim. The binned-purity selection is an oracle selection: it minimizes the RMSE computed from the true fiducial distance moduli, and the same residuals enter the covariance and effective completeness, so the headline numbers are in-sample best-case values rather than validated expectations for real surveys. No load-bearing self-citation chain is present; comparisons to Lochner et al. and other external work are not used to justify the method's validity. The Appendix A MB(z) calibration is a second oracle element (using the pure SNeIa catalog and fiducial mu(z) to remove biases), but it is transparent and standard in spirit, and it mainly sets the perfect-classifier benchmark rather than generating the 75% number. The qualitative ranking (SALT2 best, Karpenka worst) and the ML classifier scores have independent content, so this is partial circularity, not complete equivalence.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The analysis leans on the fidelity of the SNPCC simulations, the choice of an 1100-object training sample, and the assumption that thresholds tuned on simulated ground truth transfer to real data. The free parameters are the per-bin purity thresholds and per-bin MB calibrations, both fitted to the simulation's truth, plus routine ML hyperparameters.

free parameters (3)
  • Per-redshift-bin purity thresholds = 11 values, one per Delta-z=0.1 bin, shown in Figure 11 but not tabulated
    Chosen by minimizing the RMSE of the distance modulus on the test catalogs; this is a set of selection thresholds fit to the evaluation data.
  • Per-redshift-bin absolute magnitude MB(z) = 11 values, one per Delta-z=0.1 bin, shown in Figure A1
    Calibrated from the pure SNeIa catalog and the fiducial cosmology to remove light-curve fitting bias before applying the ML classifiers; these values set the zero-bias baseline for all later bias measurements.
  • ML hyperparameters = 30 random draws per model selected by RandomizedSearchCV
    For each model and catalog, 30 hyperparameter combinations were drawn and the best on validation was kept; this is ordinary model fitting but is a set of fitted choices the results depend on.
assumptions (5)
  • domain assumption SNPCC simulations faithfully represent the photometry, rates, and light-curve diversity of real surveys such as DES (Section 2).
    The entire quantitative claim is measured on these simulated lightcurves; if they are unrepresentative, the information-retention numbers do not transfer to real data.
  • domain assumption SALT2, with fixed alpha=0.11 and beta=3.2, is a valid distance estimator for SNeIa, and the fiducial flat LambdaCDM model with Omega_m=0.3 and H0=70 is the correct reference (Appendix A).
    All distance moduli, biases, and cosmological fits are computed relative to this model.
  • domain assumption The pure SNeIa catalog provides an unbiased perfect-classifier benchmark against which ML catalogs are compared.
    The perfect classifier is assumed to be the ideal sample; in reality even spectroscopically confirmed samples have selection effects and contamination.
  • domain assumption Thresholds minimizing MSE on simulated test catalogs will also minimize MSE on the real sky.
    The binned-purity method is proposed as a selection recipe; this transfer assumption is untested because the thresholds are tuned and evaluated on the same simulation.
  • domain assumption Supervised training on 1100 spectroscopically confirmed SNe is a realistic representation of spectroscopic follow-up in DES.
    The training set size and composition are fixed to 1100 SNe; the paper asserts applicability to DES based on similar numbers.

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Cite this review

Pith. "Pith review of On the cosmological performance of photometrically classified supernovae with machine learning." pith.science (2026). https://pith.science/paper/WXGQWKFO

@misc{pith2026190804210,
  author       = {Pith},
  title        = {Pith review of: On the cosmological performance of photometrically classified supernovae with machine learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WXGQWKFO}},
  note         = {Machine review of arXiv:1908.04210}
}
abstract

The efficient classification of different types of supernova is one of the most important problems for observational cosmology. However, spectroscopic confirmation of most objects in upcoming photometric surveys, such as the The Rubin Observatory Legacy Survey of Space and Time (LSST), will be unfeasible. The development of automated classification processes based on photometry has thus become crucial. In this paper we investigate the performance of machine learning (ML) classification on the final cosmological constraints using simulated lightcurves from The Supernova Photometric Classification Challenge, released in 2010. We study the use of different feature sets for the lightcurves and many different ML pipelines based on either decision tree ensembles or automated search processes. To construct the final catalogs we propose a threshold selection method, by employing a \emph{Bias-Variance tradeoff}. This is a very robust and efficient way to minimize the Mean Squared Error. With this method we were able to get very strong cosmological constraints, which allowed us to keep $\sim 75\%$ of the total information in the type Ia SNe when using the SALT2 feature set and $\sim 33\%$ for the other cases (based on either the Newling model or on standard wavelet decomposition).

Figures

Figures reproduced from arXiv: 1908.04210 by the authors.

Figure 1
Figure 1. Examples of ROC (left) and Completeness-Purity (right) curves. In this example, the completeness reaches unity at a purity of 0.5, so we do not show the region below 0.5. Generally, the completeness can be below one for a minimum purity that can be less than 0.5 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Flowchart depicting how the cross validation folding algorithm works. where the summation is over the thresholds. Typically a ML problem consists in constructing an optimized pipeline of numerical preprocessing and machine learning methods that can give the best scores, where the score function is chosen ac￾cording to the problem. As mentioned above, in this work we test the overall classification performance when o… view at source ↗
Figure 3
Figure 3. Illustration of a Bias-Variance tradeoff. The minimum RMSE (red) depends on the balance between the bias b (green) and standard devi￾ation (blue). In the region where b < 0 we show |b| in dashed green. The fact that b can be negative in our case substantially affects the optimization. variance and bias depends on the model complexity. However, since in this work we investigate how a classification problem affects th… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Example of a decision tree generated by the DecisionTreeClassifier, function from SCIKIT-LEARN library, trained on a 2000 supernovae sample using the SALT2 feature set. This graph is the output from the export_graphviz function, from sklearn.tree module. The fist line …
Figure 5
Figure 5. Figure 5: ROC curves for each feature set, without (left) and with (right) the host galaxy redshift information, for all ML techniques. The numbers in the legends correspond to the value of 1000×AUC (the area under the curve) for each case [PITH_FULL_IMAGE:figures/full_fig_p008…
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Comparison between AUC and AP for each feature set and ML method. MNRAS 000, 1–18 (2019) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Evolution of bias with the redshift for two arbitrarily chosen values of purity. Data points are slightly displaced left and right for clarity, but are all for the bin centers. The red dashed line and shaded region correspond to values and standard deviation for a perf…
Figure 9
Figure 9. Figure 9: Supernova count by bins of absolute magnitude with AUC as the optimization score. Because the classifier performs best against Type II SNe than against Types Type Ibc, for very high purities only the latter contaminants remain, and because Type II and Types Ibc are at …
Figure 10
Figure 10. Figure 10: Evolution of RMSE with the Purity, using AUC (left) and AP (right) as scores. The green line is the contribution due to the variance, the blue line is the contribution due to the bias and the red thick line is the total RMSE. The dotted gray lines are the RMSE compute…
Figure 11
Figure 11. Figure 11: Evolution of purity, RMSE and bias with redshift for the “binned purity” case and for all 4 light-curve models considered. MNRAS 000, 1–18 (2019) [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: Ωm0 and w constraints obtained for each feature set when using a constant purity (top) and choosing purity per redshift bin (bottom). The red shaded region represent the ideal case of perfect classification, for which we only have SNeIa in the final catalog. ΛCDM wCDM…

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Works this paper leans on

60 extracted references · 20 canonical work pages

  1. [1]

    Abbott T., et al., 2016, MNRAS, 460, 1270, 1601.00329

    arXiv 2016

  2. [2]

    B., Banerji M., Lahav O., Rashkov V., 2011, MNRAS, 417, 1891, 0812.3831

    Abdalla F. B., Banerji M., Lahav O., Rashkov V., 2011, MNRAS, 417, 1891, 0812.3831

    arXiv 2011

  3. [3]

    Measuring the Hubble function with standard candle clustering

    Amendola L., Quartin M., 2019, arXiv e-prints, p. arXiv:1912.10255, 1912.10255 , https://ui.adsabs.harvard.edu/abs/2019arXiv191210255A

    work page Pith review arXiv 2019

  4. [4]

    Bazin G., et al., 2009, A&A, 499, 653, 0904.1066

    work page Pith review arXiv 2009

  5. [5]

    C., 2014, Proceedings of the Third Hot-Wiring the Transient Universe Workshop, 1, 1, astro-ph/1410.8185

    Bellm E. C., 2014, Proceedings of the Third Hot-Wiring the Transient Universe Workshop, 1, 1, astro-ph/1410.8185

    arXiv 2014

  6. [6]

    arXiv:1403.5237, 1403.5237 , https://ui.adsabs.harvard.edu/abs/2014arXiv1403.5237B

    Benitez N., et al., 2014, arXiv e-prints, p. arXiv:1403.5237, 1403.5237 , https://ui.adsabs.harvard.edu/abs/2014arXiv1403.5237B

    arXiv 2014

  7. [7]

    Betoule M., et al., 2014, Astron.Astrophys., 568, A22, 1401.4064

    arXiv 2014

  8. [8]

    Birrer S., et al., 2019, MNRAS, 484, 4726, 1809.01274

    arXiv 2019

Show all 60 references
  1. [9]

    Bonvin V., et al., 2017, MNRAS, 465, 4914, 1607.01790

    2017 arXiv

  2. [10]

    R., et al., 2018, ApJ, 869, 56, 1809.06381

    Burns C. R., et al., 2018, ApJ, 869, 56, 1809.06381

    2018 arXiv

  3. [11]

    Castro T., Quartin M., 2014, MNRAS, 443, L6, 1403.0293

    2014 arXiv

  4. [12]

    Dark Univ., 13, 66, 1511.08695

    Castro T., Quartin M., Benitez-Herrera S., 2016, Phys. Dark Univ., 13, 66, 1511.08695

    2016 arXiv

  5. [13]

    J., et al., 2019, A&A, 622, A176, 1804.02667

    Cenarro A. J., et al., 2019, A&A, 622, A176, 1804.02667

    2019

  6. [14]

    Charnock T., Moss A., 2017, ApJ, 837, L28, 1606.07442

    2017 arXiv

  7. [15]

    Colin J., Mohayaee R., Sarkar S., Shafieloo A., 2011, MNRAS, 414, 264, 1011.6292

    2011 arXiv

  8. [16]

    Dahlen T., et al., 2013, ApJ, 775, 93, 1308.5353

    2013 arXiv

  9. [17]

    Dilday B., et al., 2008, ApJ, 682, 262, 0801.3297

    2008 arXiv

  10. [18]

    Fawcett T., 2004, ReCALL, 31, 1

    2004

  11. [19]

    J., Mandel K., 2013, The Astrophysical Journal, 778, 167

    Foley R. J., Mandel K., 2013, The Astrophysical Journal, 778, 167

    2013

  12. [20]

    B., 2020, Phys

    Garcia K., Quartin M., Siffert B. B., 2020, Phys. Dark Univ., 29, 100519, 1905.00746

    2020 arXiv

  13. [21]

    J., Almosallam I

    Gomes Z., Jarvis M. J., Almosallam I. A., Roberts S. J., 2018, MNRAS, 475, 331, 1712.02256

    2018 arXiv

  14. [22]

    Gordon C., Land K., Slosar A., 2007, Physical Review Letters, 99, 081301, 0705.1718 , http://adsabs.harvard.edu/abs/2007PhRvL..99h1301G

    2007 arXiv

  15. [23]

    Guy J., et al., 2007, A&A, 466, 11, astro-ph/0701828

    2007 arXiv

  16. [24]

    Howlett C., Robotham A. S. G., Lagos C. D. P., Kim A. G., 2017, ApJ, 847, 128, 1708.08236

    2017 arXiv

  17. [25]

    Huber S., et al., 2019, A&A, 631, A161, 1903.00510

    2019 arXiv

  18. [26]

    Ishida E. E. O., 2019, Nature Astronomy, 3, 680

    2019

  19. [27]

    Ishida E. E. O., de Souza R. S., 2013, MNRAS, 430, 509, 1201.6676

    2013 arXiv

  20. [28]

    G., Kirshner R

    Jha S., Riess A. G., Kirshner R. P., 2007, Astrophys.J., 659, 122, astro-ph/0612666

    2007 arXiv

  21. [29]

    O., et al., 2018, ApJ, 857, 51, 1710.00846

    Jones D. O., et al., 2018, ApJ, 857, 51, 1710.00846

    2018 arXiv

  22. [30]

    V., Feroz F., Hobson M

    Karpenka N. V., Feroz F., Hobson M. P., 2012, Monthly Notices of the Royal Astronomical Society, 429, 1278, https://academic.oup.com/mnras/article-pdf/429/2/1278/18456286/sts412.pdf

    2012

  23. [31]

    Kessler R., et al., 2009, ApJS, 185, 32, 0908.4274

    2009 arXiv

  24. [32]

    Kessler R., et al., 2010a, Publications of the Astronomical Society of the Pacific, 122, 1415–1431, 1008.1024

    arXiv

  25. [33]

    Kessler R., et al., 2010b, arXiv e-prints, 1001.5210 , https://ui.adsabs.harvard.edu/abs/2010arXiv1001.5210K

    arXiv

  26. [34]

    Kessler R., et al., 2019, MNRAS, 485, 1171, 1811.02379

    2019 arXiv

  27. [35]

    Kessler R., Scolnic D., 2017, ApJ, 836, 56, 1610.04677

    2017 arXiv

  28. [36]

    Kgoadi R., Engelbrecht C., Whittingham I., Tkachenko A., 2019, Preprint, 000, 1, 1906.06628

    2019 arXiv

  29. [37]

    S., Mota D

    Koivisto T. S., Mota D. F., Quartin M., Zlosnik T. G., 2011, Phys. Rev., D83, 023509, 1006.3321

    2011 arXiv

  30. [38]

    A., Hlozek R., 2007, Phys

    Kunz M., Bassett B. A., Hlozek R., 2007, Phys. Rev., D75, 103508, astro-ph/0611004

    2007 arXiv

  31. [39]

    D., Peiris H

    Lochner M., McEwen J. D., Peiris H. V., Lahav O., Winter M. K., 2016, ApJS, 225, 31, 1603.00882

    2016 arXiv

  32. [40]

    A., et al., 2009, arXiv e-prints, p

    LSST Science Collaboration Abell P. A., et al., 2009, arXiv e-prints, p. arXiv:0912.0201, 0912.0201 , https://ui.adsabs.harvard.edu/abs/2009arXiv0912.0201L

    2009 arXiv

  33. [41]

    M., Scovacricchi D., Bacon D., Collett T

    Macaulay E., Davis T. M., Scovacricchi D., Bacon D., Collett T. E., Nichol R. C., 2017, MNRAS, 467, 259, 1607.03966

    2017 arXiv

  34. [42]

    I., et al., 2019, AJ, 158, 171, 1809.11145 , https://ui.adsabs.harvard.edu/abs/2019AJ....158..171M

    Malz A. I., et al., 2019, AJ, 158, 171, 1809.11145 , https://ui.adsabs.harvard.edu/abs/2019AJ....158..171M

    2019 arXiv

  35. [43]

    J., 2019, arXiv e-prints, p

    Markel J., Bayless A. J., 2019, arXiv e-prints, p. arXiv:1907.00088, 1907.00088 , https://ui.adsabs.harvard.edu/abs/2019arXiv190700088M

    2019 arXiv

  36. [44]

    Mendes de Oliveira C., et al., 2019, MNRAS, 489, 241, 1907.01567 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.489..241M

    2019 arXiv

  37. [45]

    M \" o ller A., Deboiss \` i Ere T., 2018, MNRAS, 000, 1, 1901.06384v2

    2018 arXiv

  38. [46]

    arXiv:1810.06441, 1810.06441 , https://ui.adsabs.harvard.edu/abs/2018arXiv181006441M

    Moss A., 2018, arXiv e-prints, p. arXiv:1810.06441, 1810.06441 , https://ui.adsabs.harvard.edu/abs/2018arXiv181006441M

    2018 arXiv

  39. [47]

    Newling J., Bassett B., Hlozek R., Kunz M., Smith M., Varughese M., 2012, MNRAS, 421, 913, 1110.6178

    2012 arXiv

  40. [48]

    Newling J., Varughese M., Bassett B., Campbell H., Hlozek R., Kunz M., Lampeitl H., Martin B., Nichol R., Parkinson D., Smith M., 2011, MNRAS, 414, 1987, 1010.1005 , https://ui.adsabs.harvard.edu/abs/2011MNRAS.414.1987N

    2011 arXiv

  41. [49]

    J., 2010, MNRAS, 405, 2579, 1001.2037

    Oguri M., Marshall P. J., 2010, MNRAS, 405, 2579, 1001.2037

    2010 arXiv

  42. [50]

    Machine Learning Res., 12, 2825, 1201.0490

    Pedregosa F., et al., 2011, J. Machine Learning Res., 12, 2825, 1201.0490

    2011 arXiv

  43. [51]

    Quartin M., Marra V., Amendola L., 2014, Phys.Rev., D89, 023009, 1307.1155

    2014 arXiv

  44. [52]

    G., et al., 2016, ApJ, 826, 56, 1604.01424

    Riess A. G., et al., 2016, ApJ, 826, 56, 1604.01424

    2016 arXiv

  45. [53]

    B., Lahav O., 2016, Publ

    Sadeh I., Abdalla F. B., Lahav O., 2016, Publ. Astron. Soc. Pac., 128, 104502, 1507.00490

    2016 arXiv

  46. [54]

    Saito T., Rehmsmeier M., 2015, PLoS ONE, 10(3): e0118432

    2015

  47. [55]

    Sako M., et al., 2008, AJ, 135, 348, 0708.2750

    2008 arXiv

  48. [56]

    Sako M., et al., 2018, Publ. Astron. Soc. Pac., 130, 064002, 1401.3317

    2018 arXiv

  49. [57]

    M., et al., 2018, ApJ, 859, 101, 1710.00845

    Scolnic D. M., et al., 2018, ApJ, 859, 101, 1710.00845

    2018 arXiv

  50. [58]

    M., 2019, Phys

    Soltis J., Farahi A., Huterer D., Liberato C. M., 2019, Phys. Rev. Lett., 122, 091301, 1902.07189

    2019 arXiv

  51. [59]

    A., Dawes R

    Swets J. A., Dawes R. M., Monahan J., 2000, Scientific American, 283, 82, https://ui.adsabs.harvard.edu/abs/2000SciAm.283d..82S

    2000

  52. [60]

    A., et al., 2019, ApJ, 884, 83, 1905.07422 , https://ui.adsabs.harvard.edu/abs/2019ApJ...884...83V

    Villar V. A., et al., 2019, ApJ, 884, 83, 1905.07422 , https://ui.adsabs.harvard.edu/abs/2019ApJ...884...83V

    2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.