Pith. sign in

REVIEW 4 major objections 4 minor 63 references

Mitigating Model Misspecification in Simulation-Based Inference for Galaxy Clustering

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that a two-step correction — discarding summary-statistic coefficients that disagree across related simulators, then learning a distance-minimizing transformation of the rest — turns an out-of-distribution…

desk verdict Useful two-step fix for SBI misspecification, but the lambda selection rule makes the headline BOSS error bars less bulletproof than they look. read the letter →

arxiv 2507.03086 v1 pith:VXDZURG7 submitted 2025-07-03 astro-ph.CO

Sébastien Pierre , Bruno Régaldo-Saint Blancard , ChangHoon Hahn , Michael Eickenberg This is my paper
classification astro-ph.CO
keywords simulation-basedinferencemodelmisspecificationgalaxyclusteringwaveletscatteringtransformmaximummeandiscrepancyout-of-distributiondetectioncosmologicalparametersBOSSsurvey
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 whether simulation-based inference can be trusted when the single observed galaxy catalog falls outside the distribution of the training simulations, and answers yes if the summary statistics are first cleaned and then warped. It uses the wavelet scattering transform (WST) analysis of the BOSS galaxy sample as a case study, where earlier work found signs of misspecification. The proposed pipeline first discards WST coefficients whose marginal distributions differ by more than one standard deviation between two related simulators, on the grounds that such coefficients encode simulator artifacts rather than cosmology. It then learns a nonlinear transformation of the remaining coefficients, regularized so that the transformed training summaries and the transformed observation have small maximum mean discrepancy, with the regularization strength selected from a drop in posterior variability across neural architectures. The corrected analysis yields $\Omega_m = 0.32^{+0.02}_{-0.02}$ and $\sigma_8 = 0.80^{+0.02}_{-0.02}$, respectively $1.4\times$ and $3.1\times$ tighter than a standard perturbation-theory power-spectrum analysis, while restoring consistency across alternative forward models.

What carries the argument

The mechanism is a two-step correction on summary statistics. Step one is a hard filter: for each of the 3,677 WST coefficients the paper compares the marginal distributions of the TEST0 and TEST1 simulator outputs and removes any coefficient whose standardized mean difference $|\mu_0-\mu_1|/\sigma_{0/1}$ exceeds $1\sigma$, deleting just under half of the coefficients, most of them small-scale. Step two is an MMD-regularized neural posterior estimator: an MLP transformation $\eta_\psi$ maps the pruned statistics jointly with the normalizing-flow density estimator $q_\phi(\theta|\eta_\psi(s))$, while the squared maximum mean discrepancy between transformed training summaries and the single transformed observation is added to the loss with weight $\lambda$. The paper deliberately keeps $\eta_\psi$ non-invertible around the observation, so the density estimator cannot undo the correction.

What would settle it

Run the full two-step pipeline on many TEST2-style mock galaxy catalogs with known true cosmological parameters, choosing $\lambda$ separately for each mock by the $D_v$ drop. If the 68% credible intervals exclude the true parameters more than 32% of the time, or if posterior means systematically shift toward the prior centroid as $\lambda$ is raised past the $D_v$ drop, then the $\lambda$-selection rule is biased and the reported BOSS error bars cannot be trusted.

Watch

Extended reading notes

Core claim

The paper's central claim is that model misspecification detectable from a single observation can be mitigated without sacrificing most of the constraining power, and that this is what makes the corrected WST analysis reliable. On tests using the mock challenge, the hard coefficient cut removes the previously observed $\sigma_8$ bias across TEST1 and TEST2, while the MMD-regularized transformation, with $\lambda = 1$ chosen as the smallest value at which the normalized posterior-variability score $D_v$ drops, brings the BOSS observation back into the training support and suppresses the spread across equally well-trained density estimators. The resulting posterior is consistent with other galaxy-clustering analyses and is tighter than both the standard power-spectrum baseline and the SimBIG bispectrum analysis, which the paper reads as confirmation that the wavelet scattering transform carries cosmological information beyond two- and three-point statistics.

Load-bearing premise

The load-bearing premise is that the regularization strength $\lambda$ can be set from the observed data itself, using the drop in posterior variability $D_v$, without pulling the final posterior toward the center of the prior.

Editorial extensions

If this is right

  • Both steps are needed: pruning alone leaves the observation out-of-distribution, and the learned transformation alone leaves the $\sigma_8$ bias across simulators unresolved.
  • The corrected pipeline restores cross-simulator robustness, with posterior predictions for $\sigma_8$ consistent across TEST0, TEST1, and TEST2.
  • Combining the corrected posterior with a BBN prior gives derived constraints of $H_0 = 68.8^{+2.8}_{-2.6}$ and $S_8 = 0.83^{+0.04}_{-0.04}$, in agreement with CMB-based values and in slight tension with some weak-lensing measurements.
  • The tighter-than-bispectrum constraints imply the WST retains cosmological information beyond the two- and three-point functions.
  • The procedure is portable to other simulation-based inference settings and to emulator-based analyses of higher-order statistics, at the cost of breaking amortized inference.

Reading between the lines

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

  • A sharper test of the $\lambda$-selection rule than the paper's prior-robustness check would be to run the whole pipeline on many TEST2 mocks with known true parameters and verify that the reported credible intervals achieve nominal coverage; the ground-truth check currently tunes $\lambda$ on the same TEST2 sample it evaluates.
  • The same $D_v$ diagnostic could serve as a general-purpose out-of-distribution alarm for any SBI pipeline with an ensemble of density estimators, since it requires only the observation and a set of equally well-trained networks, not a bespoke mock challenge.
  • The $1\sigma$ pruning threshold is itself a tunable hyperparameter, so the method implies an explicit robustness-informativeness frontier that could be mapped by varying the threshold and measuring both cross-simulator bias and constraint width.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper addresses model misspecification in simulation-based inference (SBI) applied to galaxy clustering, using the SimBIG framework with wavelet scattering transform (WST) summaries as a case study. The authors propose a two-step mitigation: first, prune WST coefficients whose marginal distributions differ by more than 1σ between the TEST0 and TEST1 mock-challenge simulators; second, learn a neural transformation of the pruned statistics with an MMD-based regularization term whose strength λ is selected using a posterior-variability diagnostic D_v. The paper reports that the method resolves the previously identified out-of-distribution (OOD) behavior of the BOSS observation and yields ΛCDM constraints of Ω_m = 0.32 ± 0.02 and σ_8 = 0.80 ± 0.02, claimed to be 1.4× and 3.1× tighter than a standard perturbation-theory power-spectrum analysis. Validation is performed on the SimBIG mock-challenge simulators, and a prior-robustness test with a narrower Ω_m prior is presented.

Significance. If the central claim is correct, the paper offers a practical contribution to robust SBI: it provides a concrete diagnostic for OOD behavior (D_v) and a two-stage correction that preserves most of the constraining power of a rich summary statistic while improving cross-simulator robustness. The authors are appropriately candid about the risks of over-regularization, the loss of interpretability, and the breakdown of amortization. The use of the external TEST2 simulator and the explicit prior-robustness test are positive features that go beyond a purely methodological proposal. However, the load-bearing validation of the λ-selection rule currently rests on a circular use of the observed data and on an ambiguous single-realization ground-truth test. Until that validation gap is closed, the reported BOSS central values and error bars should be regarded as conditional on an untested assumption rather than as fully robust constraints.

major comments (4)
  1. [Sec. III B 3, Fig. 6; Sec. IV B 1] The regularization strength λ is selected as the smallest value at which D_v drops for the BOSS observation, and this same λ=1 is then used in Sec. IV B 1 to report the BOSS constraints. D_v is an ensemble-consistency diagnostic, not a calibration statistic: minimizing it guarantees that the 10 trained architectures agree, but it does not establish that their common posterior is centered on the true cosmology. The prior-robustness test in Sec. IV B 2 (Fig. 11) is suggestive, but both runs use the same training simulator and the same D_v-based selection rule, so a systematic pull toward the training centroid would persist under both priors. Please provide a calibration study on many TEST2 realizations in which λ is chosen by a fixed, pre-specified rule (or on a separate tuning realization) and the resulting posteriors are checked for coverage; without this, the reported credible intervals are not independent of the selection procedure.
  2. [Sec. IV A 4, Fig. 8, footnote 5] The only ground-truth check of the full method is performed on a single TEST2 realization, and the text and caption disagree: the caption states that the blue (before-correction) posterior 'appears more compatible with the true cosmological parameters,' while the text says the updated inference is more consistent, particularly for σ8. In addition, footnote 5 indicates that λ=1 was found 'in this setting,' i.e., on the same realization that is then used for evaluation, so this check does not validate the data-driven λ-selection rule. Please clarify the figure discrepancy and add an evaluation protocol that separates λ selection from evaluation.
  3. [Eq. (4), Fig. 6] The statement that D_v 'converges to 1.0, indicating that the posterior collapses to the prior for any input' appears inconsistent with the definition of D_v in Eq. (4): if all architectures returned the same prior-based posterior, the pairwise KL divergences would vanish, giving D_v=0, not 1. If the normalization in Fig. 6 is different from Eq. (4), please define it explicitly; if the plateau at 1.0 instead means that the observed posterior variability matches the validation-set reference, the text should say so, because the λ-selection argument depends on this distinction.
  4. [Sec. III A, Fig. 5] The coefficient-pruning threshold of 1σ in the standardized TEST0–TEST1 mean difference is presented without a sensitivity analysis. This threshold removes just under half of the 3,677 WST coefficients and is one of the two main ingredients of the method, so the final constraints depend on it. Please report how the robustness diagnostics and the BOSS posteriors change for nearby thresholds (e.g., 0.5σ, 2σ) or justify the threshold with an independent criterion.
minor comments (4)
  1. [Sec. II B 4 b] The D_v test is defined as 'significantly larger than a relevant reference value,' but no reference value or significance threshold is specified; please state how the reference is computed and what quantitative criterion is used to declare the test failed.
  2. [Fig. 2] The right panel is described as showing consistency across the three histograms; adding a quantitative comparison (e.g., a two-sample Kolmogorov–Smirnov statistic or the normalized means and standard deviations) would strengthen the claim beyond visual inspection.
  3. [Throughout] The notation for the variability metric alternates between 'D_v' and 'Dv'; please unify the subscript notation in the text, equations, and figures.
  4. [Sec. III B 2] The caveat that minimizing the single-observation MMD 'can lead to mapping the observation toward the centroid of the transformed training set' is important and should be explicitly recalled in the λ-selection discussion in Sec. III B 3, since it is the core failure mode the D_v-based rule is intended to avoid.

Circularity Check

2 steps flagged · score 5.0 of 10

D_v-based lambda selection makes the 'OOD resolved' claim definitional, and the TEST2 ground-truth check tunes lambda on the same realization it evaluates.

  1. self definitional [Sec. III B 3 (Setting λ); diagnostic defined in Sec. II B 4 b; applied in Sec. IV B 1]
    "Based on this behavior, we select λ as the smallest value at which Dv drops significantly. This point corresponds to the minimal regularization needed to bring the observation in-distribution... For the observed data, when λ is very small, the variability of posteriors remains high... However, at a specific threshold of λ, we observe a clear drop in Dv, signaling that η has effectively mapped the observation into the training distribution."

    D_v is the paper's operational definition of OOD: 'We consider the test to fail—and thus signal potential model misspecification—if the inferred posteriors are mutually incompatible, that is if Dv is significantly larger than a relevant reference value.' Lambda is then chosen as the smallest value at which D_v drops, and the later claim that the observation 'is no longer OOD' (Fig. 3, right) is simply the observation that the selection objective has been met. The success criterion is identical to the tuning objective, so the OOD-resolution claim holds by construction rather than by an independent test.

  2. fitted input called prediction [Sec. IV A 4 (Application on Test Data) and footnote 5; carried to BOSS in Sec. IV B 1]
    "We randomly select a simulation from TEST2... We train our pipeline on this setup and compare the resulting posteriors before and after applying our method.5 The comparison is shown in Fig. 8. The updated inference appears more consistent with the fiducial value, particularly for the σ8 parameter. [Footnote 5:] The optimal regularization strength λ in this setting is found to be λ = 1."

    The only ground-truth check of the method tunes the regularization strength λ on the very TEST2 realization it then evaluates, and the same λ=1 is carried to the BOSS analysis. Because λ controls the strength of the MMD term that pulls the observation toward the training centroid, selecting λ on the test realization and then declaring that the same realization is 'more consistent with the fiducial value' is not an independent validation: the fitted hyperparameter and the evaluated posterior come from the same data point. The prior-robustness test in Sec. IV B 2 (Fig. 11) does not remove this, since both prior runs use the same BOSS observation and the same D_v-based selection rule.

full rationale

The paper's central numerical constraints (Ω_m = 0.32^{+0.02}_{-0.02}, σ_8 = 0.80^{+0.02}_{-0.02}) are not themselves produced by equating an input to an output; they are genuine outputs of the trained NPE, and the comparison against the external perturbation-theory power-spectrum analysis [3] supplies independent context. The coefficient pruning step (Sec. III A) is checked on TEST2, which was not used for the pruning, so that part is not circular. There is no load-bearing appeal to a uniqueness theorem, and the main transformation method is adapted from an external reference [32] rather than from a self-citation. However, the paper's robustness narrative contains two circular elements. First, the D_v diagnostic is used both as the criterion for declaring the observation OOD and as the objective for selecting the regularization strength λ; the subsequent statement that the observation is no longer OOD is therefore a restatement of the selection rule rather than an independent verification. Second, the only test with a known true cosmology, the TEST2 example of Sec. IV A 4, tunes λ on the same TEST2 realization it evaluates, making the claimed improvement on that realization an artifact of tuning rather than a prediction. Because the headline claim includes 'resolves OOD issues' and 'robust cosmological inference,' and because the BOSS posterior used to report the central values is obtained with λ selected from the BOSS observation itself via D_v, the circularity is partial but real. The central values and error bars retain independent content in the sense that the NPE is not fit to the true cosmology, but the strength of the OOD-resolution claim is inflated by construction. Score 5 reflects this partial circularity, short of the 6+ level reserved for cases where the central derivation is fully forced by definition or by a self-citation chain.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The learned transformation eta_psi is a function rather than a postulated entity. The ledger is dominated by two hyperparameters (the pruning threshold and lambda), both selected using data, plus domain assumptions about the test simulators and the OOD diagnostics.

free parameters (2)
  • Coefficient pruning threshold = 1 sigma (normalized mean difference between TEST0 and TEST1 marginals)
    Chosen by hand in Sec III A; removes just under half of the 3,677 WST coefficients. The cut is not derived from theory and controls how much information is discarded.
  • Regularization strength lambda = 1 (for both the BOSS observation and the single TEST2 illustration)
    Selected in Sec III B 3 as the smallest value at which the posterior variability D_v drops significantly; selected using the observed data itself, so it is fitted to the target of inference.
assumptions (5)
  • domain assumption TEST0 and TEST1, generated with different halo finders and HOD models at the same fiducial cosmology, are representative of the model misspecification affecting BOSS; WST coefficients whose TEST0/TEST1 marginals differ by more than 1 sigma are simulator-specific artifacts.
    Load-bearing for Step 1 (Sec III A). If the true misspecification direction for BOSS is not captured by TEST0/TEST1, pruning could remove informative coefficients or keep misspecified ones.
  • domain assumption For a single observation, lying outside the finite-sample support of the training summaries, or showing high posterior variability D_v across equally well-trained NPEs, is a reliable sign of model misspecification.
    Used in Sec II A2 and Sec II B4 to justify the diagnostics; support is approximated by finite simulations, so detection is heuristic.
  • domain assumption The MMD-regularized training objective with a Gaussian kernel and median-heuristic length scale preserves enough information about theta while pulling the observation into the training support.
    Core of Step 2 (Sec III B); if the transformation class or distance is not sufficiently informative, posteriors degrade or remain biased.
  • domain assumption Simulation-based calibration on the validation set is a valid check of posterior accuracy, despite the validation set not being independent of model selection.
    Admitted in Sec IV A2; the paper says the validation set is used in place of an independent test set due to limited data.
  • standard math Squared MMD with a characteristic Gaussian kernel is a valid measure of distributional discrepancy and can be estimated with a single observation.
    Used in Sec III B2 following [32, 35].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Mitigating Model Misspecification in Simulation-Based Inference for Galaxy Clustering." pith.science (2026). https://pith.science/paper/VXDZURG7

@misc{pith2026250703086,
  author       = {Pith},
  title        = {Pith review of: Mitigating Model Misspecification in Simulation-Based Inference for Galaxy Clustering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VXDZURG7}},
  note         = {Machine review of arXiv:2507.03086}
}
abstract

Simulation-based inference (SBI) has become an important tool in cosmology for extracting additional information from observational data using simulations. However, all cosmological simulations are approximations of the actual universe, and SBI methods can be sensitive to model misspecification - particularly when the observational data lie outside the support of the training distribution. We present a method to improve the robustness of cosmological analyses under such conditions. Our approach first identifies and discards components of the summary statistics that exhibit inconsistency across related simulators, then learns a transformation that brings the observation back within the support of the training distribution. We apply our method in the context of a recent SimBIG SBI galaxy clustering analysis using the wavelet scattering transform (WST) summary statistic. The original analysis struggled to produce robust constraints for certain subsets of WST coefficients, where the observational data appeared out-of-distribution (OOD) relative to the training data. We show that our method enables robust cosmological inference and resolves OOD issues, while preserving most of the constraining power. In particular, the improved SimBIG WST analysis yields $\Lambda$CDM constraints of $\Omega_m = 0.32^{+0.02}_{-0.02}$ and $\sigma_8 = 0.80^{+0.02}_{-0.02}$, which are respectively $1.4\times$ and $3.1\times$ tighter than those from a standard perturbation-theory-based power spectrum analysis, confirming the significant information gain of WST summary statistics. The proposed method is easily applicable to other cosmological SBI contexts and represents a step toward more robust SBI pipelines.

Figures

Figures reproduced from arXiv: 2507.03086 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of model misspecification in a 2D ex [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Histograms of the normalized differences between the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Posterior predictions (68th and 95th percentile con [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4. 3D linear projection of the training data (blue) and [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Normalized posterior variability [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Empirical cumulative distribution function of the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Posterior distributions for the cosmological param [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Updated cosmological constraints on Ω [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Posterior distributions for the cosmological param [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Schematic of the [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Comparison of the [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

63 extracted references · 25 canonical work pages

  1. [14]

    Application on Test Data We illustrate the impact of our method using synthetic data that mimics an observational setting where model FIG. 8. Posterior distributions for the cosmological param- eters Ω m, Ω b, h, ns, and σ8 inferred from a single TEST2 simulation. Contours indicate the 68th and 95th percentiles. The true parameter values used to generate ...

    work page

  2. [32]

    J. Hou, A. Moradinezhad Dizgah, C. Hahn, M. Eicken- berg, S. Ho, P. Lemos, E. Massara, C. Modi, L. Parker, and B. R´ egaldo-Saint Blancard, Cosmological constraints from the redshift-space galaxy skew spectra, PhRvD109, 103528 (2024), arXiv:2401.15074 [astro-ph.CO]

    arXiv 2024

  3. [1]

    The simulator takes the form of a probabilistic model that generates data x ∈ Rn given a parameter θ ∈ Θ ⊂ Rd

    Definition SBI relies on simulations to capture the relationship between model parameters and data. The simulator takes the form of a probabilistic model that generates data x ∈ Rn given a parameter θ ∈ Θ ⊂ Rd. It is represented by a parametric family of distributions {Pθ, θ∈ Θ}. In contrast, the true data originate from an unknown process denoted by G. A...

    work page

  4. [2]

    In galaxy clustering analyses, for ex- ample, we typically have access to only a single observa- tion — one samplex drawn from the true data-generating process G

    Case of a Single Observation Detecting model misspecification in cosmology applica- tions is particularly challenging due to the limited num- ber of observations. In galaxy clustering analyses, for ex- ample, we typically have access to only a single observa- tion — one samplex drawn from the true data-generating process G. In this paper, we choose to foc...

    work page

  5. [3]

    typically limited by computational cost, it is common to map the data to a lower-dimensional space using a summary statistic

    Summary Statistics Since the full simulated data x ∈ Rn is often high- dimensional, and the number of available simulations is 2 In this work, as in most practical situations, the support of Pθ is approximated using a finite set of simulated samples. typically limited by computational cost, it is common to map the data to a lower-dimensional space using a...

    work page

  6. [4]

    • The dark matter halo finder Rockstar, which identifies dark matter halos from the simulation outputs

    Forward Model The SimBIG forward model maps cosmological param- eters θ = (Ωm, Ωb, h, ns, σ8) to synthetic galaxy catalogs x [10] using the following components: • High-resolution Quijote N -body simulations, which yield the distribution of dark matter parti- cles for different values of θ. • The dark matter halo finder Rockstar, which identifies dark mat...

    work page

  7. [5]

    Neural Posterior Estimation To perform inference on the cosmological parameters θ given summary statistics s, SimBIG employs neural posterior estimation (NPE), a family of SBI techniques that approximate the posterior distribution p(θ | s) with neural density estimators, typically normalizing flows [28, 29]. In our setting, each simulation yields a pair (...

    work page

  8. [6]

    This setup constitutes the Sim- BIG mock challenge [10], which is comprised of: • TEST0: 500 galaxy catalogs generated using the original SimBIG forward model

    Mock Challenge In addition to the forward model, the SimBIG frame- work includes a set of three test datasets designed to assess the robustness of the inference pipeline to alterna- tive modeling choices. This setup constitutes the Sim- BIG mock challenge [10], which is comprised of: • TEST0: 500 galaxy catalogs generated using the original SimBIG forward...

    work page

Show all 63 references
  1. [7]

    These issues raised concerns about the robustness of the SBI pipeline as well as the reliability of the posterior distribution obtained from the observa- tional data

    Diagnosing Model Misspecification In the WST analysis conducted in [14], two signs of model misspecification were observed: (1) biased param- eter estimates when evaluated on simulations fromTEST1 and TEST2, and (2) high variability in the observational posteriors across neura...

  2. [8]

    Building on the NPE frame- work introduced in Section II B, we assume access to pairs (θi, si) sampled from the joint distribution p(θ, s)

    Principle We briefly summarize the approach and refer the reader to [32] for full details. Building on the NPE frame- work introduced in Section II B, we assume access to pairs (θi, si) sampled from the joint distribution p(θ, s). Standard NPE methods train a neural density es...

  3. [9]

    The MMD [35] is a kernel-based measure of the discrepancy between two probability distributions, P and Q

    Choice of Distance d For practical implementation, we follow [32] and use the squared maximum mean discrepancy (MMD) as our distance d. The MMD [35] is a kernel-based measure of the discrepancy between two probability distributions, P and Q. It relies on a kernel function k : ...

  4. [10]

    8 For λ = 0, loss of Eq

    Setting λ We now discuss the importance of selecting an appro- priate value for λ and the risks associated with subopti- mal choices. 8 For λ = 0, loss of Eq. (5) reduces to the standard NPE objective of Eq. (3), with no regularization. Con- versely, setting λ extremely high c...

  5. [11]

    3 For ηψ, we choose a multi-layer perceptron architecture, detailed in Fig

    Training Procedure We train 10 different MAF architectures using the hy- perparameters identified as optimal in [14]. 3 For ηψ, we choose a multi-layer perceptron architecture, detailed in Fig. 12. Importantly, a key design goal was to prevent the transformation from being loc...

  6. [12]

    Due to the limited data, we use the validation set in place of an independent test set

    Calibration As in previous SimBIG analyses, we use simulation- based calibration (SBC) [36] to assess the accuracy of our posterior estimates. Due to the limited data, we use the validation set in place of an independent test set. For each validation sample ( ˜θ, ˜s), we draw ...

  7. [13]

    Robustness We assess the robustness of our inference method to changes in the simulator as described in Sect. II B 4. We note that while we indirectly made use of information from TEST0 and TEST1 through the hard cut on incompat- ible summary statistic coefficients, no informa...

  8. [15]

    In this setting, the optimal regulariza- 5 The optimal regularization strength λ in this setting is found to be λ = 1

    Cosmological Constraints We now present the results obtained when accounting for model misspecification in the analysis of the BOSS galaxy sample. In this setting, the optimal regulariza- 5 The optimal regularization strength λ in this setting is found to be λ = 1. 10 tion par...

  9. [16]

    A legitimate concern is that the method could bias the observational poste- rior toward the center of the prior

    Robustness to Choice of Prior Finally, we assess whether our method is sensitive to the choice of prior distribution. A legitimate concern is that the method could bias the observational poste- rior toward the center of the prior. Specifically, if the FIG. 9. Same as Fig. 8 bu...

  10. [17]

    Alsing, T

    J. Alsing, T. Charnock, S. Feeney, and B. Wandelt, Fast likelihood-free cosmology with neural density esti- mators and active learning, MNRAS 488, 4440 (2019), arXiv:1903.00007 [astro-ph.CO]

    2019 arXiv

  11. [18]

    Cranmer, J

    K. Cranmer, J. Brehmer, and G. Louppe, The frontier of simulation-based inference, Proceedings of the National Academy of Science 117, 30055 (2020), arXiv:1911.01429 [stat.ML]

    2020 arXiv

  12. [19]

    M. M. Ivanov, M. Simonovi´ c, and M. Zaldarriaga, Cos- mological parameters from the BOSS galaxy power spec- trum, JCAP 2020, 042 (2020), arXiv:1909.05277 [astro- ph.CO]

    2020 arXiv

  13. [20]

    W. L. W. Sargent and E. L. Turner, A statistical method for determining the cosmological density parameter from the redshifts of a complete sample of galaxies., ApJL212, L3 (1977)

    1977

  14. [21]

    Kaiser, Clustering in real space and in redshift space, MNRAS 227, 1 (1987)

    N. Kaiser, Clustering in real space and in redshift space, MNRAS 227, 1 (1987)

    1987

  15. [22]

    D. J. Eisenstein, W. Hu, and M. Tegmark, Cosmic Com- plementarity: H 0 and Ω m from Combining Cosmic Mi- crowave Background Experiments and Redshift Surveys, ApJL 504, L57 (1998), arXiv:astro-ph/9805239 [astro- ph]

    1998 arXiv

  16. [23]

    A. J. S. Hamilton, Linear Redshift Distortions: a Re- view, in The Evolving Universe , Astrophysics and Space Science Library, Vol. 231, edited by D. Hamilton (1998) p. 185, arXiv:astro-ph/9708102 [astro-ph]

    1998 arXiv

  17. [24]

    C. Hahn, M. Eickenberg, S. Ho, J. Hou, P. Lemos, E. Massara, C. Modi, A. Moradinezhad Dizgah, B. R´ egaldo-Saint Blancard, and M. M. Abidi, A for- ward modeling approach to analyzing galaxy clus- tering with simbig, PNAS 120, e2218810120 (2023), arXiv:2211.00723 [astro-ph.CO]

    2023 arXiv

  18. [25]

    C. Hahn, P. Lemos, L. Parker, B. R´ egaldo-Saint Blan- card, M. Eickenberg, S. Ho, J. Hou, E. Massara, C. Modi, A. Moradinezhad Dizgah, and D. Spergel, Cos- mological constraints from non-gaussian and nonlinear galaxy clustering using the simbig inference framework, 13 Nature ...

    2024 arXiv

  19. [26]

    C. Hahn, M. Eickenberg, S. Ho, J. Hou, P. Lemos, E. Massara, C. Modi, A. Moradinezhad Dizgah, B. R´ egaldo-Saint Blancard, and M. M. Abidi, Sim- BIG: mock challenge for a forward modeling ap- proach to galaxy clustering, JCAP 2023, 010 (2023), arXiv:2211.00660 [astro-ph.CO]

    2023 arXiv

  20. [27]

    D. J. Eisenstein, D. H. Weinberg, E. Agol, H. Ai- hara, C. Allende Prieto, S. F. Anderson, J. A. Arns, ´E. Aubourg, S. Bailey, E. Balbinot, et al., SDSS-III: Mas- sive Spectroscopic Surveys of the Distant Universe, the Milky Way, and Extra-Solar Planetary Systems, AJ142, 72 (2...

    2011 arXiv

  21. [28]

    K. S. Dawson, D. J. Schlegel, C. P. Ahn, S. F. Anderson, ´E. Aubourg, S. Bailey, R. H. Barkhouser, J. E. Bautista, A. Beifiori, A. A. Berlind, et al., The Baryon Oscillation Spectroscopic Survey of SDSS-III, AJ 145, 10 (2013), arXiv:1208.0022 [astro-ph.CO]

    2013 arXiv

  22. [29]

    C. Hahn, M. Eickenberg, S. Ho, J. Hou, P. Lemos, E. Massara, C. Modi, A. Moradinezhad Dizgah, L. Parker, B. R´ egaldo-Saint Blancard, and SimBIG Col- laboration, Cosmological constraints from the nonlin- ear galaxy bispectrum, PhRvD 109, 083534 (2024), arXiv:2310.15243 [astro-ph.CO]

    2024 arXiv

  23. [30]

    R´ egaldo-Saint Blancard, C

    B. R´ egaldo-Saint Blancard, C. Hahn, S. Ho, J. Hou, P. Lemos, E. Massara, C. Modi, A. Moradinezhad Diz- gah, L. Parker, Y. Yao, and M. Eickenberg, Galaxy clus- tering analysis with SimBIG and the wavelet scattering transform, PhRvD 109, 083535 (2024), arXiv:2310.15250 [astro-ph.CO]

    2024 arXiv

  24. [31]

    Lemos, L

    P. Lemos, L. Parker, C. Hahn, S. Ho, M. Eickenberg, J. Hou, E. Massara, C. Modi, A. Moradinezhad Dizgah, B. R´ egaldo-Saint Blancard, and D. Spergel, Field-level simulation-based inference of galaxy clustering with con- volutional neural networks, PhRvD 109, 083536 (2024)

    2024

  25. [33]

    Massara, C

    E. Massara, C. Hahn, M. Eickenberg, S. Ho, J. Hou, P. Lemos, C. Modi, A. Moradinezhad Diz- gah, L. Parker, and B. R´ egaldo-Saint Blancard, Sim- BIG: Cosmological Constraints using Simulation-Based Inference of Galaxy Clustering with Marked Power Spec- tra, arXiv e-prints 10.4...

    2024 doi arXiv

  26. [34]

    C. Hahn, F. Villaescusa-Navarro, E. Castorina, and R. Scoccimarro, Constraining M ν with the bispectrum. Part I. Breaking parameter degeneracies, JCAP 2020, 040 (2020), arXiv:1909.11107 [astro-ph.CO]

    2020 arXiv

  27. [35]

    Hahn and F

    C. Hahn and F. Villaescusa-Navarro, Constraining M ν with the bispectrum. Part II. The information content of the galaxy bispectrum monopole, JCAP 2021, 029 (2021), arXiv:2012.02200 [astro-ph.CO]

    2021 arXiv

  28. [36]

    Eickenberg, E

    M. Eickenberg, E. Allys, A. Moradinezhad Dizgah, P. Lemos, E. Massara, M. Abidi, C. Hahn, S. Hassan, B. Regaldo-Saint Blancard, S. Ho, S. Mallat, J. And´ en, and F. Villaescusa-Navarro, Wavelet Moments for Cos- mological Parameter Estimation, arXiv e-prints (2022), arXiv:2204....

    2022 arXiv

  29. [37]

    Valogiannis and C

    G. Valogiannis and C. Dvorkin, Towards an opti- mal estimation of cosmological parameters with the wavelet scattering transform, PhRvD 105, 103534 (2022), arXiv:2108.07821 [astro-ph.CO]

    2022 arXiv

  30. [38]

    Massara, F

    E. Massara, F. Villaescusa-Navarro, C. Hahn, M. M. Abidi, M. Eickenberg, S. Ho, P. Lemos, A. M. Dizgah, and B. R´ egaldo-Saint Blancard, Cosmological Informa- tion in the Marked Power Spectrum of the Galaxy Field, ApJ 951, 70 (2023), arXiv:2206.01709 [astro-ph.CO]

    2023 arXiv

  31. [39]

    J. Hou, A. Moradinezhad Dizgah, C. Hahn, and E. Mas- sara, Cosmological information in skew spectra of bi- ased tracers in redshift space, JCAP 2023, 045 (2023), arXiv:2210.12743 [astro-ph.CO]

    2023 arXiv

  32. [40]

    C. Modi, S. Pandey, M. Ho, C. Hahn, B. R´ egaldo- Saint Blancard, and B. Wandelt, Sensitivity Analysis of Simulation-Based Inference for Galaxy Clustering, MN- RAS 10.1093/mnras/stae2473 (2024), arXiv:2309.15071 [astro-ph.CO]

    2024 arXiv

  33. [41]

    Y. Jo, S. Genel, A. Sengupta, B. Wandelt, R. Somerville, and F. Villaescusa-Navarro, Towards Robustness Across Cosmological Simulation Models TNG, SIMBA, ASTRID, and EAGLE, arXiv e-prints (2025), arXiv:2502.13239 [astro-ph.CO]

    2025 arXiv

  34. [42]

    Anau Montel, J

    N. Anau Montel, J. Alvey, and C. Weniger, Tests for model misspecification in simulation-based inference: From local distortions to global model checks, PhRvD 111, 083013 (2025), arXiv:2412.15100 [astro-ph.IM]

    2025 arXiv

  35. [43]

    A. E. Bayer, F. Villaescusa-Navarro, S. Sharief, R. Teyssier, L. H. Garrison, L. Perreault-Levasseur, G. L. Bryan, M. Gatti, and E. Visbal, Field-Level Comparison and Robustness Analysis of Cosmological N-Body Simu- lations, arXiv e-prints (2025), arXiv:2505.13620 [astro- ph.CO]

    2025 arXiv

  36. [44]

    Papamakarios, E

    G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mo- hamed, and B. Lakshminarayanan, Normalizing flows for probabilistic modeling and inference, JMLR 22, 1 (2021), arXiv:1912.02762 [stat.ML]

    2021 arXiv

  37. [45]

    Kobyzev, S

    I. Kobyzev, S. D. Prince, and M. A. Brubaker, Normal- izing flows: An introduction and review of current meth- ods, IEEE Transactions on Pattern Analysis & Machine Intelligence 43, 3964 (2021), arXiv:1908.09257 [stat.ML]

    2021 arXiv

  38. [46]

    Y. Yao, B. R´ egaldo-Saint Blancard, and J. Domke, Simulation-based stacking, in Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, Vol. 238, edited by S. Dasgupta, S. Mandt, and Y. Li (PMLR, 20...

    2024

  39. [47]

    Lakshminarayanan, A

    B. Lakshminarayanan, A. Pritzel, and C. Blundell, Sim- ple and scalable predictive uncertainty estimation us- ing deep ensembles, in Advances in Neural Information Processing Systems , Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vish- wanat...

  40. [49]

    Huang, A

    D. Huang, A. Bharti, A. Souza, L. Acerbi, and S. Kaski, Learning robust statistics for simulation-based inference under model misspecification, in Advances in Neural In- formation Processing Systems , Vol. 36, edited by A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and...

    2023

  41. [50]

    Tzeng, J

    E. Tzeng, J. Hoffman, N. Zhang, K. Saenko, and T. Darrell, Deep Domain Confusion: Maximizing for Do- main Invariance, arXiv e-prints (2014), arXiv:1412.3474 [cs.CV]

    2014 arXiv

  42. [51]

    Cannon, D

    P. Cannon, D. Ward, and S. M. Schmon, Investi- 14 gating the impact of model misspecification in neu- ral simulation-based inference, CoRR abs/2209.01845 (2022)

    2022 arXiv

  43. [52]

    Gretton, K

    A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Sch¨ olkopf, and A. Smola, A kernel two-sample test, Journal of Ma- chine Learning Research 13, 723 (2012)

    2012

  44. [53]

    Talts, M

    S. Talts, M. Betancourt, D. Simpson, A. Vehtari, and A. Gelman, Validating bayesian inference al- gorithms with simulation-based calibration (2020), arXiv:1804.06788 [stat.ME]

    2020 arXiv

  45. [54]

    Abdalla, G

    E. Abdalla, G. F. Abell´ an, A. Aboubrahim, A. Agnello, ¨O. Akarsu, Y. Akrami, G. Alestas, D. Aloni, L. Amen- dola, L. A. Anchordoqui, et al. , Cosmology intertwined: A review of the particle physics, astrophysics, and cos- mology associated with the cosmological tensions and ...

    2022 arXiv

  46. [55]

    E. Aver, K. A. Olive, and E. D. Skillman, The effects of He I λ10830 on helium abundance determinations, JCAP 2015, 011 (2015), arXiv:1503.08146 [astro-ph.CO]

    2015 arXiv

  47. [56]

    R. J. Cooke, M. Pettini, and C. C. Steidel, One Percent Determination of the Primordial Deuterium Abundance, ApJ 855, 102 (2018), arXiv:1710.11129 [astro-ph.CO]

    2018 arXiv

  48. [57]

    Sch¨ oneberg, J

    N. Sch¨ oneberg, J. Lesgourgues, and D. C. Hooper, The BAO+BBN take on the Hubble tension, JCAP2019, 029 (2019), arXiv:1907.11594 [astro-ph.CO]

    2019 arXiv

  49. [58]

    O. H. E. Philcox and M. M. Ivanov, BOSS DR12 full- shape cosmology: Λ CDM constraints from the large- scale galaxy power spectrum and bispectrum monopole, PhRvD 105, 043517 (2022), arXiv:2112.04515 [astro- ph.CO]

    2022 arXiv

  50. [59]

    S.-F. Chen, Z. Vlah, and M. White, A new analysis of galaxy 2-point functions in the BOSS survey, in- cluding full-shape information and post-reconstruction BAO, JCAP 2022, 008 (2022), arXiv:2110.05530 [astro- ph.CO]

    2022 arXiv

  51. [60]

    Asgari, C.-A

    M. Asgari, C.-A. Lin, B. Joachimi, B. Giblin, C. Hey- mans, H. Hildebrandt, A. Kannawadi, B. St¨ olzner, T. Tr¨ oster, J. L. van den Busch, A. H. Wright, M. Bil- icki, C. Blake, J. de Jong, A. Dvornik, T. Erben, F. Get- man, H. Hoekstra, F. K¨ ohlinger, K. Kuijken, L. Miller, ...

    2021 arXiv

  52. [61]

    A. Amon, D. Gruen, M. A. Troxel, N. MacCrann, S. Do- delson, A. Choi, C. Doux, L. F. Secco, S. Samuroff, E. Krause, J. Cordero, J. Myles, J. DeRose, R. H. Wechsler, M. Gatti, A. Navarro-Alsina, G. M. Bern- stein, B. Jain, J. Blazek, A. Alarcon, A. Fert´ e, P. Lemos, M. Raveri,...

    2022

  53. [62]

    L. F. Secco, S. Samuroff, E. Krause, B. Jain, J. Blazek, M. Raveri, A. Campos, A. Amon, A. Chen, C. Doux, A. Choi, D. Gruen, G. M. Bernstein, C. Chang, J. DeRose, J. Myles, A. Fert´ e, P. Lemos, D. Huterer, J. Prat, M. A. Troxel, N. MacCrann, A. R. Lid- dle, T. Kacprzak, X. Fa...

    2022 arXiv

  54. [63]

    Valogiannis, S

    G. Valogiannis, S. Yuan, and C. Dvorkin, Precise cos- 15 mological constraints from BOSS galaxy clustering with a simulation-based emulator of the wavelet scattering transform, PhRvD 109, 103503 (2024), arXiv:2310.16116 [astro-ph.CO]. 16 Appendix A: Additional Figures s (2073)...

    2024 arXiv

  55. [2017]

    arXiv:1612.01474 [stat.ML]

    arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.