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Investigating the Influence of Asymmetric Errors on Retrievals of Exoplanet Transmission Spectra

T0 review · 2 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read At the error-bar asymmetries seen in current JWST data (up to 77% in WASP-39b), the standard Gaussian likelihood used in exoplanet retrievals is safe; bias appears only as average asymmetry nears 80%, and an asymmetric likelihood cannot…

desk verdict Solid sensitivity analysis showing Gaussian likelihoods are safe for current JWST asymmetry levels, with a real convention bug in the split-normal implementation and a shape-dependence caveat. read the letter →

arxiv 2507.19223 v1 pith:INGIXQR2 submitted 2025-07-25 astro-ph.EP astro-ph.IM

Jack J. Davey , Kai Hou Yip , Quentin Changeat , Ingo P. Waldmann This is my paper · ORCID
classification astro-ph.EPastro-ph.IM
keywords transmissionspectroscopyatmosphericretrievalGaussianlikelihoodasymmetricerrorssplitnormaldistributionJWSTWASP-39bBayesianinference
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

Transmission-spectrum retrievals of exoplanet atmospheres almost always assume a Gaussian likelihood, which implicitly treats the upper and lower error bars on every spectral point as equal. This paper tests that assumption by injecting asymmetric noise into simulated WASP-39b spectra and retrieving the atmosphere with both a symmetric Gaussian likelihood and an asymmetric split-normal likelihood, whose widths above and below the mode follow the reported upper and lower errors. At the asymmetry levels present in the real JWST NIRSpec G395H observation of WASP-39b (average 5.7%, maximum 77%), the two samplers return statistically indistinguishable posteriors, supporting the paper's conclusion that the Gaussian assumption is safe for current datasets. The bias becomes critical only at larger asymmetries (for example an average of 80%), where the Gaussian likelihood misses the true parameters while the asymmetric sampler recovers them. The paper further establishes that three summary statistics (a median plus upper and lower error bars) do not uniquely determine the shape of the noise distribution, so an asymmetric likelihood is only reliable when its assumed shape matches the true noise.

What carries the argument

The comparison is carried by two likelihoods: the standard Gaussian, and a split-normal likelihood, which joins two half-Gaussians of different widths at a central mode and assigns one width to residuals above the model and the other to residuals below, with asymmetry measured as $\mathrm{asym} = 100\%(\sigma_\uparrow-\sigma_\downarrow)/\min(\sigma_\uparrow,\sigma_\downarrow)$. Against these are tested several injected noise distributions, including a 'custom' asymmetric distribution built by PCHIP interpolation through the 16th, 50th and 84th percentiles with exponentially decaying tails, standing in for the true but unknown noise. Because the simulations have known ground truth, the displacement of each posterior from the true input values measures the bias introduced by the likelihood choice for that noise case, and the two-sample Kolmogorov-Smirnov statistic quantifies agreement between the Gaussian and asymmetric retrievals.

What would settle it

Take the full MCMC posterior samples from the lightcurve fits of a real JWST observation (not just the median and 16th/84th percentile summaries), propagate them into the atmospheric retrieval, and compare the resulting posterior on a parameter such as the water abundance or planetary radius with the retrieval that uses a Gaussian likelihood on the summary statistics alone; if the two differ by more than 1σ, the Gaussian assumption is not safe at currently observed asymmetry levels.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Gaussian likelihood assumption is safe to keep for current exoplanet transmission-spectrum retrievals, and that it becomes dangerous only at error-bar asymmetries larger than those now observed. The evidence comes from retrievals on simulated WASP-39b spectra built to mimic the JWST NIRSpec G395H observation reported by Carter et al. (2024): when noise is injected at the observed asymmetry levels, the Gaussian and split-normal likelihoods produce posteriors that agree (small two-sample Kolmogorov-Smirnov statistics), and both recover the true parameters. When the same simulations are run with extreme forced asymmetries (+125% per point with error bars scaled by 1.5), the Gaussian likelihood misses the true planetary radius, isothermal temperature, and molecular abundances by more than 1σ, while the split-normal likelihood recovers them; the deviation of the Gaussian retrieval grows smoothly with the injected asymmetry. A further result is that the shape of the asymmetric distribution matters as much as its degree of asymmetry: an asymmetric sampler applied to noise drawn from a differently shaped asymmetric distribution (a 'custom' distribution built by percentiles) still biases the retrieval even at matching asymmetry levels. The paper concludes that reporting a median plus upper and lower bounds is insufficient to characterise the noise and advocates publishing complete lightcurve posteriors.

Load-bearing premise

The safety conclusion rests on the assumption that the 'custom' asymmetric noise distribution constructed from the median and the 16th/84th percentile error bars is a faithful stand-in for the true shape of lightcurve-posterior asymmetries; the paper's own appendix shows three summary statistics do not determine a distribution, so a differently shaped but equally asymmetric true noise could produce retrieval bias even at the asymmetry levels seen in WASP-39b.

Editorial extensions

If this is right

  • Retrievals on the published WASP-39b NIRSpec G395H spectrum, and on datasets with comparable or smaller error-bar asymmetry, can be quoted with the Gaussian likelihood: the split-normal retrieval agrees with it, with Kolmogorov-Smirnov statistics near zero.
  • If future datasets reach average asymmetries around 80% (or per-point asymmetries of +125% with inflated errors), a Gaussian retrieval will systematically miss the true radius, temperature, and molecular abundances, and the width of its posterior will give no warning that it is biased.
  • An asymmetric likelihood is not a general fix: when applied to noise whose shape differs from the assumed split normal, it still biases parameters even though the asymmetry levels match, so its predictions are only trustworthy when the full noise shape is known.
  • Spectral resolution does not change the conclusions: binning the same simulation to the HST WFC3 grid with a forced +77% asymmetry keeps the two samplers in agreement, so the results should carry over to other instruments.
  • Reports giving only a median plus upper and lower error bars cannot support a shape-correct asymmetric likelihood; the paper shows the minimum requirement is the full posterior, since distinct distributions share identical 16th, 50th and 84th percentiles.

Reading between the lines

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

  • An extension the paper does not run is the direct propagation of full lightcurve MCMC posteriors into the retrieval; given the shape degeneracy shown in its appendix, that is the only route to a shape-correct asymmetric likelihood from real data, and it would test the safety claim on archival JWST observations beyond WASP-39b.
  • The safety threshold the paper identifies (negligible bias at 77% maximum, critical near 80% average) is established for one dataset and one noise construction; a generalisable test would check whether the threshold tracks a specific statistical moment such as skewness of the injected distributions, allowing observers to screen any spectrum for vulnerability before running a retrieval.
  • Combining an asymmetric likelihood with modelling of inter-wavelength correlated noise, which the paper lists as future work, could reveal whether the two neglected effects compound or partially cancel in real JWST data; the simulations here treat each spectral point independently.
  • If the community followed the paper's recommendation to publish full lightcurve posteriors, the added information would also make direct lightcurve-to-atmosphere fitting more tractable, since the paper notes that approach is currently limited mainly by dimensionality and the lossiness of summary statistics.
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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

2 major / 6 minor

Summary. The paper tests whether the standard Gaussian likelihood used in exoplanet transmission-spectrum retrievals introduces bias when the reported per-wavelength error bars are asymmetric. It defines an asymmetry measure, demonstrates on a sine-wave toy model that asymmetric (split-normal) noise can bias Gaussian retrievals of amplitude and offset parameters, and then runs TauREx3 retrievals on simulated WASP-39b NIRSpec G395H-like spectra under four noise schemes (Gaussian, split-normal, custom PCHIP distribution, compression) and two asymmetry regimes (extreme +125% and realistic up to 77%). The authors compare Gaussian and split-normal likelihood samplers using emcee and report that the posteriors agree closely at realistic asymmetry levels but diverge at extreme asymmetry, that the shape of the noise distribution matters when the likelihood shape is misspecified, and that three summary statistics do not uniquely determine the asymmetric distribution. They conclude that it is safe to continue using the Gaussian likelihood for current datasets, while recommending propagation of full lightcurve posteriors as future work.

Significance. If the central claim holds, the paper provides useful reassurance for current JWST retrieval pipelines and a quantitative warning about future data. The paper's strengths are its known ground-truth simulations, the clear separation of 'noise' and 'sampling' distributions, the repeated-realization consistency checks in Appendix B, and the quantitative KS comparisons. The acknowledgment in Appendix A that three summary statistics are insufficient to fix the noise shape is an honest and important contribution. The main limitation is that the 'safe for current datasets' conclusion is conditional on an assumed (custom PCHIP and exponential-tail) noise shape that is not validated against actual lightcurve posteriors; this is acknowledged in Section 4.1 but needs to be carried into the abstract and the central claims.

major comments (2)
  1. [Section 2.5] The description of the split-normal likelihood is internally inconsistent with the definition in Eq. (4). The text says: 'for each data point we determine whether the data lie above or below the model being tested and then add a contribution to our sum with the appropriate sigma value based on the outcome of this test (sigma_down if the data sits above the model and sigma_up otherwise).' But Eq. (4) defines sigma = sigma_up when x > mu, and Figure 3 states that the widths above and below the median are set by sigma_up and sigma_down respectively. Thus, if the data lie above the model, the likelihood should use sigma_up, not sigma_down. This is load-bearing: if the code follows the text, the asymmetric sampler uses a mirrored split-normal likelihood, so the 'known noise' experiments in Sections 3.2 and Appendix B are not actually matching the generative distribution, and the proof-of-concept results in Sections 3.1 and 3.2 would need to be re-evaluated. If the code follows Eq. (4), the text is wrong. Please correct one or the other, verify with the code, and confirm that the reported retrievals (Figures 4, 6, B1, B2, and Table 4) use the intended orientation.
  2. [Abstract, Section 3.4, Section 4.1, Appendix A] The central safety claim ('it is safe to use the Gaussian likelihood assumption for current datasets') is supported only for the custom noise shape built in Section 2.1(iv) by PCHIP interpolation through the 16th, 50th and 84th percentiles with exponentially decaying tails. Appendix A explicitly shows that three summary statistics do not uniquely determine an asymmetric distribution, and Section 4.1 restricts the study to artificial noise cases. A different but equally plausible asymmetric shape with the same reported percentiles (for example, a heavier-tailed or differently skewed distribution) could produce a larger Gaussian-versus-asymmetric bias at the observed maximum asymmetry of 77%. The abstract overstates the conclusion; it should be softened to 'safe for the noise shapes considered here' or supported by an additional robustness test that perturbs the assumed shape at realistic asymmetry levels. The paper's own future-work item in Section 4.1 is exactly the validation that the safety claim needs.
minor comments (6)
  1. [Section 2.2] The sentence 'Their values are sigma_up and sigma_down for the lower and upper errorbars respectively' appears to reverse the upper/lower mapping relative to Eq. (4) and Figure 3; please reword to avoid confusion.
  2. [Abstract] The phrase 'an average asymmetry of 80%' is not tied to a clearly described experiment in the main text; the extreme cases use a constant +125% asymmetry and Section 3.4 sweeps between +12.5% and +125%. Please specify what the 80% scenario is and whether 'average' means a constant asymmetry applied to every point.
  3. [Table 4 and Appendix C] The two-sample KS quantity is described both as a 'measure of the probability that our two samples are drawn from the same underlying distribution' and as a test statistic taking values from 0 to 1. These two descriptions are inconsistent; the 0-1 quantity is the KS statistic D (a distance), not a probability. Please state which quantity is reported and, if p-values are used, interpret them accordingly.
  4. [Section 2.4] The phrase 'randomly sample from a normal distribution centered on the data point' is ambiguous; it presumably means sampling a noisy value around the noiseless model point (i.e., additive noise centered at zero), but as written it suggests drawing from a distribution centered on the already noisy point. Please clarify.
  5. [Figure 9] The asymmetry sweep in Figure 9 does not state how many noise realizations are used at each asymmetry value or whether a single realization is shown. Given that the effect is small near the 77% JWST maximum, please report the realization count or add repeated draws to support the trend.
  6. [Data Availability] Simulated data are only 'available upon request' and no code or random seeds are provided; given the stochastic nature of the experiments, releasing the retrieval code or seeds would materially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: an empirical simulation study whose safety conclusion is produced by forward modeling with known inputs, not by fitting or by a self-citation chain.

full rationale

This paper is an empirical simulation study, not a derivation. The central claim (Gaussian likelihoods are safe at current asymmetry levels) is established by generating noisy simulated spectra with known input atmospheric parameters and comparing retrieval posteriors under Gaussian and split-normal likelihoods. All noise injections are specified from first principles in Sections 2.1-2.4, and no parameter is fitted to the target conclusion and then renamed as a prediction. The 'known noise' split-normal/split-normal retrieval in Section 3.2 is a consistency check, not a prediction: the likelihood matches the generative distribution by design, and the paper uses it only to demonstrate that the Gaussian likelihood is biased under large, perfectly characterized asymmetry. The realistic case in Section 3.4 uses a custom PCHIP noise distribution built from the 16th, 50th and 84th percentiles of the Carter et al. (2024) data, while the Gaussian and split-normal likelihoods are also built from those summary statistics; the small KS statistics in Table 4 are outputs of the simulation, not inputs. If anything, the safety conclusion is limited by an assumption about the true shape of the lightcurve posteriors, a limitation explicitly acknowledged in Section 4.1 ('In this work, we have only considered artificial noise cases') and demonstrated in Appendix A, where three summary statistics are shown not to determine a unique distribution. Such an assumption is a robustness limitation, not a circularity. The only self-citation is the use of TauREx3 as the forward model generator; this tool is shared by both likelihoods and is not the source of the Gaussian-versus-asymmetric comparison. No equation reduces to its own input, and no fitted parameter is presented as a prediction. Therefore no circularity is present.

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

The central claim rests on a set of standard statistical assumptions, the TauREx3 atmospheric forward model, and the ad hoc construction of the custom noise distribution. No new physical entities are introduced, but the noise-shape assumption is the most fragile input because the paper itself shows that the reported summary statistics underdetermine the distribution.

free parameters (3)
  • Custom CDF tail decay rate = not specified
    The custom asymmetric noise distribution in Section 2.1(iv) uses exponentially decaying tails beyond the 16th and 84th percentiles, but no decay rate is reported. This choice affects the tail weight and therefore the shape-sensitivity results, so it is an ad hoc modeling choice that the central claim depends on.
  • Compression noise asymmetry formula = asym_i = -50 * (X_i - min(X)) / (max(X) - min(X))
    Used in Sections 2.2 and 2.4 to create a noise case that compresses the spectrum toward the baseline. The formula and its -50 scaling are chosen by hand to test a specific bias pattern.
  • Extreme asymmetry levels = +125%, +77%, +50%, +12.5%
    The paper applies several hand-chosen asymmetry levels and error-bar scaling factors (e.g., 1.5x) to probe regimes. These are experimental design parameters, not fitted to data, but they define the conditions under which the conclusions are drawn.
assumptions (5)
  • standard math Bayes' theorem and the validity of MCMC sampling for the posterior
    Used throughout as the retrieval framework (Eq 1 and Section 2.5). Assumed standard.
  • standard math The split-normal distribution with the normalization constant A = sqrt(2/pi) * (sigma_up + sigma_down)^{-1}
    Defined in Eq (4) and used as the likelihood. This is a standard two-piece normal distribution.
  • domain assumption The reported transit-depth central value is the median and the reported errors are the 16th and 84th percentiles
    The custom CDF construction in Section 2.1(iv) relies on this assumption, which the authors note is common in the field for ExoTIC-JEDI reduced data.
  • domain assumption The TauREx3 forward model with isothermal profile, constant abundances, opaque cloud deck, and H2/He ratio 0.17:1 represents a realistic WASP-39b atmosphere
    The simulated spectra in Section 2.3 use these modeling choices. The retrieved bias could in principle depend on the atmospheric model, though the paper's conclusions are mainly about the noise statistics.
  • ad hoc to paper The custom PCHIP-and-exponential-tail distribution is a valid representation of plausible lightcurve-posterior noise
    Introduced in Section 2.1(iv) specifically for this study. The paper acknowledges that this shape is chosen to emphasize disagreements and that three summary statistics do not uniquely determine the true distribution (Appendix A).

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Cite this review

Pith. "Pith review of Investigating the Influence of Asymmetric Errors on Retrievals of Exoplanet Transmission Spectra." pith.science (2026). https://pith.science/paper/INGIXQR2

@misc{pith2026250719223,
  author       = {Pith},
  title        = {Pith review of: Investigating the Influence of Asymmetric Errors on Retrievals of Exoplanet Transmission Spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/INGIXQR2}},
  note         = {Machine review of arXiv:2507.19223}
}
read the original abstract

In studies of exoplanet atmospheres using transmission spectroscopy, Bayesian retrievals are the most popular form of analysis. In these procedures it is common to adopt a Gaussian likelihood. However, this implicitly assumes that the upper and lower error bars on the spectral points are equal. With recent observations from the James Webb Space Telescope (JWST) offering higher quality of data, it is worth revisiting this assumption to understand the impact that an asymmetry between the error bars may have on retrieved parameters. In this study, we challenge the approximation by comparing retrievals using a symmetric, Gaussian likelihood, and an asymmetric, split normal likelihood. We find that the influence of this assumption is minimal at the scales of asymmetry observed in JWST observations of WASP-39 b (with a maximum asymmetry of 77%) but we show that it would become critical with greater levels of asymmetry (e.g. an average asymmetry of 80%). Furthermore, we stress the importance of the shape of the asymmetric distribution and the difficulty in fitting this distribution from three summary statistics (the median and an upper and lower bound on the transit depth). An asymmetric likelihood sampler will incorrectly predict parameters if the shape of the likelihood does not match that of the underlying noise distribution even when the levels of asymmetry are equal in both. Overall, we find that it is safe to use the Gaussian likelihood assumption for current datasets but it is worth considering the potential bias if greater asymmetries are observed.

Figures

Figures reproduced from arXiv: 2507.19223 by the authors.

Figure 1
Figure 1. An observation of WASP-39 b with the JWST NIRSpec G395H instrument as published by Carter et al. (2024). Data cover both the NRS1 and NRS2 detectors hence the gap observed between 3.7 µm and 3.8 µm. This dataset contains different values for the upper and lower error bars on each spectral point and, in this plot, cases where the percentage asymmetry between these values exceeds 15%, 35% or 55% have been indicated by… view at source ↗
Figure 2
Figure 2. The simulated datasets for the four noise cases on the sine wave model. With reference to equation 6, the true values for a, b and c are 0.5,0.75 and 0 respectively. In each panel, the black dashed line displays the true, underlying model and the coloured points show the noisy data. From top to bottom, the sine wave data have noise added according to the Gaussian case, the asymmetric shift case, the asymmetric compr… view at source ↗
Figure 3
Figure 3. An example of the noise distribution and the approximation with the split normal distribution for a point in the Carter et al. (2024) dataset for WASP-39 b observed with JWST’s NIRSpec G395H instrument. We use the example of the point with the highest level of asymmetry between its upper and lower error bars (-77.21%). The Gaussian distribution (shown in red) is parameterised by 𝜇 and 𝜎 which are the median (set by … view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Comparative corner plots for each of the noisy datasets for the sine wave example. In each corner plot, true values are indicated by the horizontal and vertical black lines. The solid outlines in black display the results of the retrieval with the Gaussian likelihood a…
Figure 5
Figure 5. Figure 5: The simulated datasets for the four noise schemes for the sine wave model. In each panel, the black dashed line displays the true, underlying model, the purple lines show a random sample of 500 of the output solutions and the coloured points show the noisy data. From t…
Figure 6
Figure 6. Figure 6: Retrieved results for both sampling methods when noise is added to the NIRSpec G395H WASP-39 b simulation using to a split normal distribu￾tion with a +125% asymmetry and where the observed error bars are scaled by a factor of 1.5. Dashed lines represent the 16th, 50th…
Figure 7
Figure 7. Figure 7: Retrieval results comparing the different sampling techniques on data where noise is added with either a Gaussian or a custom (asymmetric) distribution. In the right-hand corner plot, the noise is scaled to be representative of that reported in the Carter et al. (2024)…
Figure 8
Figure 8. Figure 8: The retrieved spectra and input data for the case of extreme asymmetry (+125% on each spectral point and error bars scaled by a factor of 1.5) when retrieving with a Gaussian likelihood (blue line) or an asymmetric likelihood (yellow line). The black dashed line in the…
Figure 9
Figure 9. Figure 9: The deviation from the true value of the retrieved isothermal tem￾perature and planetary radius as the level of asymmetry in the dataset is varied. These simulations of WASP-39 b with JWST’s NIRSpec G395H instrument had noise added according to a custom distribution bu…
Figure 11
Figure 11. Figure 11: Retrieved results for both sampling methods when the NIRSpec G395H WASP-39 b simulation had nosie added according to a split normal distribution designed to preferentially add noise to the signal towards the baseline of the spectrum (the compression noise case). Dashe…
Figure 10
Figure 10. Figure 10: Retrieved results for both sampling methods when the NIRSpec G395H WASP-39 b simulation had noise added according to a split normal distribution with a +125% asymmetry and a scaling factor of 1.5 applied to the noise distribution on every point. Dashed lines represent…
Figure 12
Figure 12. Figure 12: Retrieved results for both sampling methods when the NIRSpec G395H WASP-39 b simulation had nosie added according to a custom distri￾bution with realistic error bars and levels of asymmetry. Dashed lines repre￾sent the 16th, 50th, and 84th percentiles for the posterio…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.