Debiasing inference in large-scale structure with non-flat volume measures

Alexander Reeves; Henry Zheng; Pierre Zhang

REVIEW 3 major objections 4 minor 3 cited by

Debiasing inference in large-scale structure with non-flat volume measures

T0 review · 3 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 With the right volume measure, posterior means become unbiased on average.

desk verdict The debiasing measure's flagship claim doesn't survive a one-parameter check: the source term vanishes at the mode, leaving the mode bias uncorrected. read the letter →

arxiv 2507.20991 v1 pith:USSXUVOI submitted 2025-07-28 astro-ph.CO

Alexander Reeves , Pierre Zhang , Henry Zheng This is my paper

classification astro-ph.CO MSC 62F1562E2062F12 PACS 98.80.-k

keywords volumeprojectioneffectsnon-flatmeasureposteriormeanbiasLaplaceexpansionJeffreyspriorEFTofLSSgalaxyclusteringBayesianinference

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 targets volume projection effects: when many nuisance parameters are marginalized, the mean of a marginal posterior can shift by 1-2 $\sigma$ even when the data are informative. For posteriors that admit a Laplace expansion, the authors prove that defining expectation values with respect to a non-flat measure removes the leading-order average bias of the posterior mean, leaving bias only at $O(n^{-2})$ and retaining the leading-order Cramér-Rao variance. The construction is invariant under reparametrization, so reported numbers no longer depend on an arbitrary flat coordinate choice. In BOSS- and DESI-like mock analyses, the prescription recovers fiducial cosmological parameters below 0.1 $\sigma$ where flat-measure marginals are off by 1-2 $\sigma$.

What carries the argument

The Laplace expansion of the posterior $P(\theta\,|\,y)$ about its mode $\theta_*$, with $n$ as a formal large-sample bookkeeper, together with the Gaussian generating functional $G[j] = \int d^N\delta\, n^{-1/2}\exp(-\tfrac{1}{2}\delta^T F\delta + j^T\delta)$, carries the calculation. The central object is the volume measure $M_H = \sqrt{\det H}\, d^N\theta$ with $H_{\mu\nu}(\theta) = -\partial_{\mu\nu}\log P(\theta\,|\,y = m_*)$, the Hessian of the log-posterior at the data value $m_* = m(\theta_*)$. The log-determinant of $H$ contributes a term proportional to $F^{-1}_{\nu\rho}F_{\mu\nu;\rho}$ at $O(n^{-1})$ in the posterior mean, which cancels the flat-measure bias exactly; the Jeffreys measure $\sqrt{\det F}$ cancels only the large-$N$ enhanced part. The relevant expansion parameter is $\epsilon \sim \alpha/\sigma$, the ratio of model second derivatives to the noise-scaled signal.

What would settle it

Using noiseless synthetic data at $n=1$ in a model with a known truth and strong nonlinear coupling such that $\epsilon \sim \alpha/\sigma$ exceeds $1/3$, average the $M_H$ posterior mean over many data realizations; the paper predicts a residual bias comparable to $\sigma$, so a small bias would falsify the stated failure criterion.

Watch

Extended reading notes

Core claim

The central claim is that an unbiased estimator of the true parameter can be built directly from the posterior by choosing the integration measure $M_H = \sqrt{\det H}\, d^N\theta$, where $H_{\mu\nu}(\theta) = -\partial_{\mu\nu}\log P(\theta\,|\,y = m_*)$ is the Hessian of the log-posterior evaluated at the noise-free data prediction $m_*$ of the mode. Averaged over data samples, the posterior mean defined with this measure has zero bias through $O(n^{-1})$ and saturates the leading-order Cramér-Rao variance. The proof expands the posterior about its mode via Laplace's method and shows that the new measure contributes a term that exactly cancels the known $O(n^{-1})$ bias of the flat-measure mean; it also cancels the large-$N$ enhanced part of that bias, which is the part that grows with the number of marginalized nuisance parameters. The paper argues that this measure, unlike a flat Lebesgue measure, is invariant under reparametrization, so the quoted credible intervals do not depend on the coordinate choice of the parameter space.

Load-bearing premise

The proof requires the posterior to satisfy the Laplace conditions of appendix A (a single smooth mode, bounded derivatives, exponentially decaying tails, and positive Hessian determinant at the mode) and the expansion parameter $\epsilon \sim \alpha/\sigma$ to stay below about $1/3$; if the high-dimensional EFTofLSS posteriors violate these, the $O(n^{-1})$ cancellation does not follow.

Editorial extensions

If this is right

Volume projection effects in EFTofLSS-type analyses can be removed by adding a log-measure weight $\tfrac{1}{2}\log\det H$ to each posterior sample, without changing the posterior or the likelihood.
Post-debiasing the flat-measure mean with equation (3.3) recovers the leading-order unbiased result; in noiseless LSS mocks it brings biases from roughly $0.5$-$0.9\sigma$ down to below $0.15\sigma$.
The Jeffreys measure $\sqrt{\det F}$ is sufficient when the dominant bias is the large-$N$ enhanced part coming from linear nuisance parameters coupled to the parameters of interest.
The optimal measure $M_H$ corrects residual nonlinear-parameter bias as well, reaching below $0.1\sigma$ in the DESI-like $w_0w_a$CDM mock where flat-measure bias reaches $1.7\sigma$.
The expansion parameter $\epsilon \sim \alpha/\sigma$ can be used as a priori criterion: when it exceeds about $1/3$, the paper finds that bias is large under every volume measure considered.

Reading between the lines

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

A natural next-order test, not carried out here, is to compute the $O(n^{-2})$ average bias of $E_{P,M_H}[\theta]$ from the appendix B moments and check whether the same cancellation persists beyond leading order.
Because $H$ depends on the mode and hence on the data, the optimal measure is an empirical construction; a fully data-independent choice would be the Jeffreys measure, and the paper's results suggest Jeffreys is nearly sufficient when nuisance parameters are mostly linear.
The method could plausibly be extended to bounded or positively constrained parameters, such as neutrino mass or amplitude parameters, by starting from a log-measure on the bounded parameter; the authors explicitly leave this case for future study.
The connection to nonlinear reparametrization methods suggests that combining iterative decorrelation with one-step non-flat weighting might correct beyond-leading-order bias more cheaply, but this remains to be tested.

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.

Desk Editor's Note

read the letter

Dear Colleague,

The headline claim is that the non-flat measure MH of eq. (3.19) makes marginal posterior means unbiased to O(n^{-2}). I don't think that claim is true, and the problem is visible already in a one-parameter model with m(θ)=θ+αθ², flat prior, y ~ N(0,1).

The source of trouble is eq. (2.17). The quantity j_μ is defined with Δ_* = y − m(θ*), and the whole expansion is around the posterior mode. But the score equation at the mode forces ∂_μ m(θ*)^T C^{-1}(y − m(θ*)) = 0, so j_μ(θ*) ≡ 0 for every data realization. The paper then uses ⟨j_μ j_ν⟩ = F_{μν} to get the O(n^{-1}) bias (3.3). That variance is simply zero if j is evaluated at the mode. The derivation of the bias and the cancellation in sec. 3.3 are built on this inconsistency.

The one-parameter model makes the failure concrete. For the flat measure, the exact small-α expansion gives an average posterior mean bias of −4α (which, coincidentally, matches the paper's (3.3)). The mode itself is biased at −α. The MH measure should cancel the total bias, but when you compute its derivative correctly you get (1/2)∂ log det H = 3α, not the 4α claimed in eq. (3.22). As a result the MH-weighted mean equals the mode to O(α), so the average bias is −α, not zero. The mode bias is left uncorrected.

I want to give credit where it's due. The paper is on a real problem that matters for EFTofLSS analyses of BOSS/DESI, and the large-N enhancement argument in sec. 3.5 is a genuinely useful way to understand why projection effects can grow with the number of nuisance parameters. The mock analyses show that non-flat measures reduce the mean bias substantially in practice, even if the theoretical claim of unbiasedness is too strong. The citation practice seems fair.

The soft spots beyond the core flaw: the "least biased / minimum variance" optimality is asserted, not proven; the companion paper with the code is not available, and no code is released, so the mocks are not independently reproducible; the residual biases in the tables have no sampling uncertainties.

Who is this for? Someone working on volume projection effects in cosmology may find the empirical part useful. But the central theorem as stated should not be taken as established. I would send it to referees, since the topic is timely and the error is specific enough to be addressed, but the authors should expect a request for major revision—the theoretical claims need to be scaled back or fixed.

Referee Report

3 major / 4 minor

Summary. The paper claims that for posteriors admitting a Laplace expansion, defining posterior expectation values with the non-flat volume measure M_H = sqrt(det H) d^N theta, where H_{mu nu} = - d_{mu nu} log P(theta | y = m*), makes the posterior mean unbiased on average up to O(n^{-2}) and attains the leading-order Cramer-Rao variance. The derivation proceeds by expanding the posterior around the mode, computing average biases of the mean and mode, and showing that the measure contribution cancels the leading average mean bias. The paper then applies this prescription to noiseless EFTofLSS mock analyses, reporting that flat-measure projection effects of 1-2 sigma are reduced below 0.1 sigma with the non-flat measures.

Significance. If the central theorem were correct, the paper would provide a practical and theoretically motivated way to reduce volume projection effects in high-dimensional cosmological analyses, and the PyBird-JAX differentiable pipeline and explicit BOSS/DESI mocks are valuable assets. The exposition is clear and the Laplace algebra is worked out in detail. However, the central claim is not established: the derivation uses a source term that vanishes identically at the posterior mode, and the cancellation argument in Sec. 3.3 omits the second-order term that generates the mode bias. A direct one-parameter expansion shows that the proposed measure leaves an O(n^{-1}) bias, contradicting the claimed O(n^{-2}) unbiasedness. The empirical mock results may still indicate a useful heuristic, but the theoretical guarantee that is the paper's main result is unsupported.

major comments (3)

[Sec. 2.3, Eqs. (2.15), (2.17), and Sec. 3.1, Eq. (3.1)] The source term j_mu(theta) in Eq. (2.17) is n^{1/2} j_mu(theta) = d_mu m(theta)^T C^{-1}(y - m(theta*)). At the posterior mode theta*, the score vanishes by Eq. (3.5); with a flat prior, this gives j_mu(theta*) identically zero for every data realization. Therefore the Gaussian average in Eq. (3.1), <j_mu j_nu> = F_{mu nu}, is inconsistent with the definition of j. The expansion (2.15) around the mode should have no linear term, and the average mean bias in Eq. (3.3) is not obtained by the source-averaging procedure used in Sec. 3.1. A correct expansion around the mode produces the mean-relative-to-mode bias through the cubic and quartic terms in the exponent, not through a nonzero linear source, so the derivation of the central bias formula is not justified.
[Sec. 3.3, Eqs. (3.10)-(3.13)] The cancellation that removes the mode bias is based on an incomplete expansion. Eq. (3.10) expands Delta_* = y - m* and keeps only the linear term in delta-dagger = theta* - theta-dagger, but the quadratic term from m(theta-dagger) - m(theta*) is O(n^{-1}) and is precisely the term that produces the O(n^{-1}) mode bias in Eq. (3.8). Consequently Eq. (3.12), which writes n^{-1/2} F^{-1} j as n^{-1/2} F^{-1} j-dagger - n^{-1/2} delta-dagger, ignores the fact that j-dagger = F delta-dagger + O(delta-dagger^2); the average of the omitted O(delta-dagger^2) term is not negligible and is of the same order as the mode bias. The claimed result <E> contains -<delta-dagger> is therefore an algebraic artifact. A direct check in a one-parameter model with log-prior -tau theta^2/2 and m(theta) = theta + alpha theta^2, y ~ N(0,1), gives for the flat-measure mean bias -alpha s^2(1+3s) with s = (1+tau)^{-1}, whereas Eq. (3.3) gives -4 alpha s^2; the MH-weighted mean retains an O(alpha) bias. This contradicts the central O(n^{-2}) unbiasedness claim.
[Sec. 3.4, Eqs. (3.19), (3.21)-(3.23)] The measure M_H is constructed from H(theta) = -d^2 log P(theta | y = m*), which depends on the posterior mode theta*. The calculation in Eqs. (3.21)-(3.23) shows only that the measure contributes a term that can cancel the source-averaged bias (3.3). But since the mode itself is biased by Eq. (3.8), and since the argument that this mode bias is canceled by a source correction fails as explained above, the measure cannot make the mean unbiased relative to the truth to O(n^{-2}). The proof of the main theorem therefore hinges on the invalid step in Sec. 3.3; the mocks in Sec. 4 do not repair this because they are noiseless and do not isolate the mode-bias contribution.

minor comments (4)

[Appendix D] The text reads 'Shur complements formula'; this should be 'Schur complements formula'.
[Sec. 5] In the bullet on reparametrization, 'repametrisation' is a typo for 'reparametrization'.
[Sec. 3.3] The word 'mispecified' should be 'misspecified'.
[Sec. 4.2] The phrase 'we have eluded bias in the variance' should likely be 'we have elided bias' or 'we have not addressed bias'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the debiasing measure is an explicit algebraic construction, not a fitted prediction; the only self-citation is the companion numerical pipeline.

full rationale

The paper's central result is a constructive existence proof: given an asymptotically normal posterior, the volume measure MH = sqrt(det H) d^N theta with H_{mu nu} = -d_{mu nu} log P(theta|y=m*) is shown to cancel the leading O(n^{-1}) bias of the posterior mean. The cancellation is obtained by explicit computation: the Laplace expansion (2.15) yields the Lebesgue bias (3.3), the expansion of the measure (3.20) yields the corrective term (3.23), and eq. (3.22) identifies the log-det derivative of H with the same Fisher-derivative combination appearing in the bias. This is an algebraic identity, not a parameter fitted to data, so the unbiasedness claim is a theorem whose proof is self-contained. The mock LSS results are numerical illustrations of the derived correction, not independent predictions, and the paper does not present them as falsifying tests. The only self-citation, the companion PyBird-JAX paper [1], supplies the differentiable likelihood implementation used for the numerical demonstrations; it is not load-bearing for the analytic derivation. The paper explicitly flags its own limitation in sec. 5: for expansion parameter epsilon >~ 1/3, bias remains large under every volume measure (and for misspecified models, eq. (3.18) gives an uncorrected theoretical bias); these are stated limitations rather than circular reductions. A possible mathematical inconsistency (the source j_mu defined in eq. (2.17) vanishes at the mode by eq. (3.5), while eq. (3.1) assigns it variance F_{mu nu}) would affect the validity of the derivation, but it is not a circularity: the conclusion is not assumed as an input. Accordingly, no circular step is identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The analytic derivation contains no fitted constants; the only hand-chosen numbers are prior widths, a convergence threshold, and analysis cuts in the mock campaign, which affect the size of the demonstrated effect but not the proof. The derivation relies on standard asymptotic results and the explicit domain assumptions listed above.

free parameters (3)

EFT nuisance prior widths = Gaussian widths of order O(b1); width 5 for c2
Chosen by hand in sec. 4.2 for the mock analyses; they set the volume projected onto the cosmological parameters and thus the size of the demonstrated bias, but they do not enter the analytic proof.
Convergence threshold epsilon = ~1/3
Empirical diagnostic stated in sec. 5: the correction works when the curvature coupling relative to the posterior width is below about 1/3; this threshold is read off the mock experiments, not derived.
kmax analysis cut = 0.20 h/Mpc
Chosen for all LSS mocks in sec. 4.2; standard EFTofLSS choice, affects the numerical results but not the derivation.

assumptions (6)

domain assumption The posterior is asymptotic normal and satisfies the Laplace-method conditions of Appendix A: smooth, unimodal, with exponentially decaying tails and positive-definite Hessian at the mode.
Invoked in secs. 2.2-2.3 and Appendix A; all bias formulas (2.24), (3.3), (3.8), and (3.23) require this.
domain assumption Data y is generated by a Gaussian likelihood with known covariance C from a well-specified model, with no model misspecification.
Stated in sec. 2; eq. (3.18) shows misspecification adds an uncorrected bias.
domain assumption Sample averages over repeated experiments are equivalent to averages over independent spatial patches, the fair sample hypothesis.
Footnote 1 and sec. 2.2; this turns 'unbiased on average' into a meaningful frequentist statement in cosmology.
domain assumption Flat prior in the analytic derivations; Gaussian naturalness priors in the LSS mocks.
Secs. 2, 3.3, and 4.2; the prior affects the mode and the posterior volume through eqs. (3.15)-(3.17).
domain assumption The one-loop EFTofLSS redshift-space power spectrum with the specified 12-parameter set is the exact data-generating model for the synthetic mocks.
Secs. 4.1-4.2; if the model were wrong, the noiseless mocks would not isolate volume projection effects.
standard math Bernstein-von Mises theorem ensures convergence to a multivariate normal posterior in the large-n limit.
Sec. 2.2, used to justify asymptotic normality and the Laplace expansion.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Debiasing inference in large-scale structure with non-flat volume measures." pith.science (2026). https://pith.science/paper/USSXUVOI

@misc{pith2026250720991,
  author       = {Pith},
  title        = {Pith review of: Debiasing inference in large-scale structure with non-flat volume measures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/USSXUVOI}},
  note         = {Machine review of arXiv:2507.20991}
}

abstract

Increasingly large parameter spaces, used to more accurately model precision observables in physics, can paradoxically lead to large deviations in the inferred parameters of interest -- a bias known as volume projection effects -- when marginalising over many nuisance parameters. For posterior distributions that admit a Laplace expansion, we show that this artefact of Bayesian inference can be mitigated by defining expectation values with respect to a non-flat volume measure, such that the posterior mean becomes unbiased on average. We begin by finding a measure that ensures the mean is an unbiased estimator of the mode. Although the mode itself, as we rediscover, is biased under sample averaging, this choice yields the least biased estimator due to a cancellation we clarify. We further explain why bias in marginal posteriors can appear relatively large, yet remains correctable, when the number of nuisances is large. To demonstrate our approach, we present mock analyses in large-scale structure (LSS) wherein cosmological parameters are subject to large projection effects (at the 1-2$\sigma$ level) under a flat measure, that are however recovered at high fidelity ($<0.1\sigma$) when estimated using non-flat counterparts. Our cosmological analyses are enabled by $\texttt{PyBird-JAX}$, a fast, differentiable pipeline for LSS developed in our companion paper [1].

Figures

Figures reproduced from arXiv: 2507.20991 by the authors.

**Figure 2.** Volume measure comparison on BOSS mock data — Top panels: Marginal cosmological posteriors from ΛCDM fits to BOSS-like synthetic data, where ωb is held fixed. The total effective volume Veff = 10 Gpc3 , is subdivided in one, two, or four skies (see table 1), wherein the number of marginalised nuisance parameters increases from 12, 24, to 48, enhancing, under a flat measure, volume projection effects on the inferred … view at source ↗

**Figure 3.** Volume measure comparison on DESI mock data — Top panels: Marginal cosmological posteriors from w0waCDM fits to DESI-like synthetic data, where ωb and ns are held fixed. The total effective volume Veff = 63 Gpc3 is subdivided in seven skies (see table 2), corresponding to a total of 84 marginalised nuisance parameters. Compared to the flat measure (grey contours), which exhibits volume projection effects up to the ∼… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Diagrammatic representation of source vertices and Fisher propagators [PITH_FULL_IMAGE:figures/full_fig_p032_4.png]

**Figure 5.** Figure 5: Master rule 1 — ⟨jµjν⟩ = Fµν, ⟨jµjνρ⟩ = F µ νρ, . . . ⟨ ⟩ µ gµ ν gν = µ F −1 µρ ν F −1 σν Fρσ ≡ µ ν F −1 µν [PITH_FULL_IMAGE:figures/full_fig_p033_5.png]

**Figure 6.** Figure 6: Master rule 2 — ⟨gµgν⟩ = F −1 µν , where gµ = F −1 µρ jρ Gaussian prior π(θ) reads lnP(θ) = − 1 2 (m(θ) − y) · C −1 · (m(θ) − y) + ln π(θ) , (D.1) ln π(θ) = − 1 2 (ψα − ψˆ α) · C−1 αβ · (ψβ − ψˆ β) + ln Π(Ω) , (D.2) where the prior π consists in a multivariate Gaussian…

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization
astro-ph.CO 2026-07 unverdicted novelty 6.0 of 10

Jeffreys prior over EFTofLSS coefficients mitigates projection effects in DESI DR1 power spectrum multipole fits, recentering posteriors for late-time expansion parameters.
Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization
astro-ph.CO 2026-07 accept novelty 6.0 of 10

A hybrid Jeffreys+baseline prior removes multi-σ prior-volume projection in DESI DR1 full-shape fits of H0, w0, and wa, yielding late-time expansion constraints consistent with HOD-informed Bayesian and frequentist analyses.
A sound horizon independent measurement of $H_0$ from BOSS, DESI and DES Y3
astro-ph.CO 2026-02 conditional novelty 6.0 of 10

Combining BOSS power spectrum and bispectrum with DESI and DES lensing data yields a sound-horizon-free H0 = 70.2 ± 2.3 km/s/Mpc, with a 1.8σ BAO scale deviation that is scale-cut dependent.

Reference graph

Works this paper leans on

78 extracted references · 21 canonical work pages · cited by 2 Pith papers

[1]

Reeves, P

A. Reeves, P. Zhang and H. Zheng, PyBird-JAX: Accelerated inference in large-scale structure with model-independent emulation of one-loop galaxy power spectra , - (2025)

work page 2025
[2]

B. L. Welch and H. W. Peers, On formulae for confidence points based on integrals of weighted likelihoods, Journal of the Royal Statistical Society. Series B (Methodological) 25 (1963) 318–329

work page 1963
[3]

H. W. Peers, On confidence points and bayesian probability points in the case of several parameters , Journal of the Royal Statistical Society: Series B (Methodological) 27 (12, 2018) 9–16

work page 2018
[4]

N. Reid, R. Mukerjee and D. A. S. Fraser, Some aspects of matching priors , Lecture Notes-Monograph Series 42 (2003) 31–43

work page 2003
[5]

J. O. Berger, J. M. Bernardo and D. Sun, The formal definition of reference priors , The Annals of Statistics 37 (2009) 905 – 938

work page 2009
[6]

D’Agostini, Bayesian reasoning in high-energy physics: Principles and applications , CERN Yellow Reports: Monographs (7, 1999)

G. D’Agostini, Bayesian reasoning in high-energy physics: Principles and applications , CERN Yellow Reports: Monographs (7, 1999)

work page 1999
[7]

J. N. Fry and E. Gaztanaga, Biasing and hierarchical statistics in large scale structure , Astrophys. J. 413 (1993) 447–452, [ astro-ph/9302009]

arXiv 1993
[8]

A. F. Heavens, S. Matarrese and L. Verde, The Nonlinear redshift-space power spectrum of galaxies , Mon. Not. Roy. Astron. Soc. 301 (1998) 797–808, [ astro-ph/9808016]. 12We thank Guido d’Amico for pointing to us this fact. 34

work page Pith review arXiv 1998

Show all 78 references

[9]

McDonald, Dark matter clustering: a simple renormalization group approach , Phys

P. McDonald, Dark matter clustering: a simple renormalization group approach , Phys. Rev. D 75 (2007) 043514, [ astro-ph/0606028]

2007 arXiv
[10]

McDonald and A

P. McDonald and A. Roy, Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS, JCAP 08 (2009) 020, [ 0902.0991]

2009 arXiv
[11]

Baumann, A

D. Baumann, A. Nicolis, L. Senatore and M. Zaldarriaga, Cosmological Non-Linearities as an Effective Fluid, JCAP 07 (2012) 051, [ 1004.2488]

2012 arXiv
[12]

Senatore, Bias in the Effective Field Theory of Large Scale Structures , JCAP 11 (2015) 007, [1406.7843]

L. Senatore, Bias in the Effective Field Theory of Large Scale Structures , JCAP 11 (2015) 007, [1406.7843]

2015 arXiv
[13]

D’Amico, J

G. D’Amico, J. Gleyzes, N. Kokron, K. Markovic, L. Senatore, P. Zhang et al., The Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure , JCAP 05 (2020) 005, [ 1909.05271]

2020 arXiv
[14]

D’Amico, Y

G. D’Amico, Y. Donath, M. Lewandowski, L. Senatore and P. Zhang, The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure , JCAP 05 (2024) 059, [2206.08327]

2024 arXiv
[15]

M. M. Ivanov, M. Simonovi´ c and M. Zaldarriaga, Cosmological Parameters from the BOSS Galaxy Power Spectrum, JCAP 05 (2020) 042, [ 1909.05277]

2020 arXiv
[16]

Simon, P

T. Simon, P. Zhang, V. Poulin and T. L. Smith, Consistency of effective field theory analyses of the BOSS power spectrum, Phys. Rev. D 107 (2023) 123530, [ 2208.05929]

2023 arXiv
[18]

R. E. Kass, The Geometry of Asymptotic Inference , Statistical Science 4 (1989) 188 – 219

1989
[19]

McCullagh, Tensor Methods in Statistics

P. McCullagh, Tensor Methods in Statistics . Chapman and Hall, London, 1987

1987
[20]

Carrilho, C

P. Carrilho, C. Moretti and A. Pourtsidou, Cosmology with the EFTofLSS and BOSS: dark energy constraints and a note on priors , JCAP 01 (2023) 028, [ 2207.14784]

2023 arXiv
[21]

Donald-McCann, R

J. Donald-McCann, R. Gsponer, R. Zhao, K. Koyama and F. Beutler, Analysis of unified galaxy power spectrum multipole measurements, Mon. Not. Roy. Astron. Soc. 526 (2023) 3461–3481, [ 2307.07475]

2023 arXiv
[22]

Zhao et al., A multitracer analysis for the eBOSS galaxy sample based on the effective field theory of large-scale structure, Mon

R. Zhao et al., A multitracer analysis for the eBOSS galaxy sample based on the effective field theory of large-scale structure, Mon. Not. Roy. Astron. Soc. 532 (2024) 783–804, [ 2308.06206]

2024 arXiv
[24]

Maus, S.-F

M. Maus, S.-F. Chen and M. White, A comparison of template vs. direct model fitting for redshift-space distortions in BOSS , JCAP 06 (2023) 005, [ 2302.07430]

2023 arXiv
[25]

Maus et al., An analysis of parameter compression and Full-Modeling techniques with Velocileptors for DESI 2024 and beyond , JCAP 01 (2025) 138, [ 2404.07312]

M. Maus et al., An analysis of parameter compression and Full-Modeling techniques with Velocileptors for DESI 2024 and beyond , JCAP 01 (2025) 138, [ 2404.07312]. 35

2025 arXiv
[26]

Zhang, M

H. Zhang, M. Bonici, G. D’Amico, S. Paradiso and W. J. Percival, HOD-informed prior for EFT-based full-shape analyses of LSS , JCAP 04 (2025) 041, [ 2409.12937]

2025 arXiv
[27]

Paradiso, M

S. Paradiso, M. Bonici, M. Chen, W. J. Percival, G. D’Amico, H. Zhang et al., Reducing nuisance prior sensitivity via non-linear reparameterization, with application to EFT analyses of large-scale structure, 2412.03503

arXiv
[28]

Planck collaboration, P. A. R. Ade et al., Planck intermediate results. XVI. Profile likelihoods for cosmological parameters, Astron. Astrophys. 566 (2014) A54, [ 1311.1657]

2014 arXiv
[29]

Handley and P

W. Handley and P. Lemos, Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio, Phys. Rev. D 100 (2019) 043504, [ 1902.04029]

2019 arXiv
[30]

Joachimi et al., KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis , Astron

B. Joachimi et al., KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis , Astron. Astrophys. 646 (2021) A129, [2007.01844]

2021 arXiv
[31]

Krause et al., Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation, 2105.13548

DES collaboration, E. Krause et al., Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation, 2105.13548

arXiv
[32]

Hadzhiyska, K

B. Hadzhiyska, K. Wolz, S. Azzoni, D. Alonso, C. Garc ´ ıa-Garc ´ ıa, J. Ruiz-Zapatero et al.,Cosmology with 6 parameters in the Stage-IV era: efficient marginalisation over nuisance parameters , 2301.11895

arXiv
[33]

Gariazzo, M

S. Gariazzo, M. Archidiacono, P. F. de Salas, O. Mena, C. A. Ternes and M. T´ ortola, Neutrino masses and their ordering: Global Data, Priors and Models , JCAP 03 (2018) 011, [ 1801.04946]

2018 arXiv
[34]

J. A. D. Diacoumis and Y. Y. Y. Wong, On the prior dependence of cosmological constraints on some dark matter interactions , JCAP 05 (2019) 025, [ 1811.11408]

2019 arXiv
[35]

Herold, E

L. Herold, E. G. M. Ferreira and E. Komatsu, New Constraint on Early Dark Energy from Planck and BOSS Data Using the Profile Likelihood , Astrophys. J. Lett. 929 (2022) L16, [ 2112.12140]

2022 arXiv
[36]

J. S. Cruz, S. Hannestad, E. B. Holm, F. Niedermann, M. S. Sloth and T. Tram, Profiling cold new early dark energy , Phys. Rev. D 108 (2023) 023518, [ 2302.07934]

2023 arXiv
[37]

E. B. Holm, L. Herold, S. Hannestad, A. Nygaard and T. Tram, Decaying dark matter with profile likelihoods, Phys. Rev. D 107 (2023) L021303, [ 2211.01935]

2023 arXiv
[38]

Camarena, F.-Y

D. Camarena, F.-Y. Cyr-Racine and J. Houghteling, Confronting self-interacting neutrinos with the full shape of the galaxy power spectrum , Phys. Rev. D 108 (2023) 103535, [ 2309.03941]

2023 arXiv
[39]

Chebat et al., Cosmological neutrino mass: a frequentist overview in light of DESI , 2507.12401

D. Chebat et al., Cosmological neutrino mass: a frequentist overview in light of DESI , 2507.12401

arXiv
[40]

Robnik and U

J. Robnik and U. Seljak, Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis, Entropy 24 (2022) 1328, [ 2207.06784]

2022 arXiv
[41]

A. E. Bayer and U. Seljak, The look-elsewhere effect from a unified Bayesian and frequentist perspective, JCAP 10 (2020) 009, [ 2007.13821]

2020 arXiv
[42]

Garcia-Bellido, An Analytical Approach to Bayesian Evidence Computation , Universe 9 (2023) 118, [2301.13783]

J. Garcia-Bellido, An Analytical Approach to Bayesian Evidence Computation , Universe 9 (2023) 118, [2301.13783]. 36

2023 arXiv
[43]

J. J. M. Carrasco, M. P. Hertzberg and L. Senatore, The Effective Field Theory of Cosmological Large Scale Structures, JHEP 09 (2012) 082, [ 1206.2926]

2012 arXiv
[44]

Weinberg, Adiabatic modes in cosmology, Phys

S. Weinberg, Adiabatic modes in cosmology, Phys. Rev. D 67 (2003) 123504, [ astro-ph/0302326]

2003 arXiv
[45]

Peloso and M

M. Peloso and M. Pietroni, Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure , JCAP 05 (2013) 031, [ 1302.0223]

2013 arXiv
[46]

Kehagias and A

A. Kehagias and A. Riotto, Symmetries and Consistency Relations in the Large Scale Structure of the Universe, Nucl. Phys. B 873 (2013) 514–529, [ 1302.0130]

2013 arXiv
[47]

Creminelli, J

P. Creminelli, J. Nore˜ na, M. Simonovi´ c and F. Vernizzi,Single-Field Consistency Relations of Large Scale Structure, JCAP 12 (2013) 025, [ 1309.3557]

2013 arXiv
[48]

Perko, L

A. Perko, L. Senatore, E. Jennings and R. H. Wechsler, Biased Tracers in Redshift Space in the EFT of Large-Scale Structure, 1610.09321

arXiv
[49]

D’Amico, Y

G. D’Amico, Y. Donath, M. Lewandowski, L. Senatore and P. Zhang, The one-loop bispectrum of galaxies in redshift space from the Effective Field Theory of Large-Scale Structure , JCAP 07 (2024) 041, [2211.17130]

2024 arXiv
[50]

R. A. Porto, L. Senatore and M. Zaldarriaga, The Lagrangian-space Effective Field Theory of Large Scale Structures, JCAP 05 (2014) 022, [ 1311.2168]

2014 arXiv
[51]

Senatore and M

L. Senatore and M. Zaldarriaga, The IR-resummed Effective Field Theory of Large Scale Structures , JCAP 02 (2015) 013, [ 1404.5954]

2015 arXiv
[52]

D. J. Eisenstein, H.-j. Seo, E. Sirko and D. Spergel, Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak , Astrophys. J. 664 (2007) 675–679, [astro-ph/0604362]

2007 arXiv
[53]

White, Reconstruction within the Zeldovich approximation , Mon

M. White, Reconstruction within the Zeldovich approximation , Mon. Not. Roy. Astron. Soc. 450 (2015) 3822–3828, [ 1504.03677]

2015 arXiv
[54]

Nguyen, F

N.-M. Nguyen, F. Schmidt, B. Tucci, M. Reinecke and A. Kosti´ c, How Much Information Can Be Extracted from Galaxy Clustering at the Field Level? , Phys. Rev. Lett. 133 (2024) 221006, [2403.03220]

2024 arXiv
[55]

Spezzati, M

F. Spezzati, M. Marinucci and M. Simonovi´ c, Equivalence of the field-level inference and conventional analyses on large scales , 2507.05378

arXiv
[56]

Angulo, M

R. Angulo, M. Fasiello, L. Senatore and Z. Vlah, On the Statistics of Biased Tracers in the Effective Field Theory of Large Scale Structures , JCAP 09 (2015) 029, [ 1503.08826]

2015 arXiv
[57]

Assassi, D

V. Assassi, D. Baumann, D. Green and M. Zaldarriaga, Renormalized Halo Bias , JCAP 08 (2014) 056, [1402.5916]

2014 arXiv
[58]

Mirbabayi, F

M. Mirbabayi, F. Schmidt and M. Zaldarriaga, Biased Tracers and Time Evolution , JCAP 07 (2015) 030, [1412.5169]

2015 arXiv
[59]

DESI collaboration, A. G. Adame et al., DESI 2024 II: sample definitions, characteristics, and two-point clustering statistics , JCAP 07 (2025) 017, [ 2411.12020]. 37

2025 arXiv
[60]

Abdul Karim et al., DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints , 2503.14738

DESI collaboration, M. Abdul Karim et al., DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints , 2503.14738

arXiv
[61]

Alam et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample , Mon

BOSS collaboration, S. Alam et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample , Mon. Not. Roy. Astron. Soc. 470 (2017) 2617–2652, [ 1607.03155]

2017 arXiv
[62]

D’Amico, L

G. D’Amico, L. Senatore and P. Zhang, Limits on wCDM from the EFTofLSS with the PyBird code , JCAP 01 (2021) 006, [ 2003.07956]

2021 arXiv
[63]

DESI collaboration, A. G. Adame et al., DESI 2024 V: Full-Shape Galaxy Clustering from Galaxies and Quasars , 2411.12021

2024 arXiv
[64]

D. J. Bartlett, L. Kammerer, G. Kronberger, H. Desmond, P. G. Ferreira, B. D. Wandelt et al., A precise symbolic emulator of the linear matter power spectrum , Astron. Astrophys. 686 (2024) A209, [2311.15865]

2024 arXiv
[65]

C. Sui, D. J. Bartlett, S. Pandey, H. Desmond, P. G. Ferreira and B. D. Wandelt, SYREN-NEW: Precise formulae for the linear and nonlinear matter power spectra with massive neutrinos and dynamical dark energy , Astron. Astrophys. 698 (2025) A1, [ 2410.14623]

2025 arXiv
[66]

Foreman-Mackey, D

D. Foreman-Mackey, D. W. Hogg, D. Lang and J. Goodman, emcee: The MCMC Hammer , Publ. Astron. Soc. Pac. 125 (2013) 306–312, [ 1202.3665]

2013 arXiv
[67]

Creminelli, G

P. Creminelli, G. Signorelli and A. Strumia, Frequentist analyses of solar neutrino data , JHEP 05 (2001) 052, [ hep-ph/0102234]

2001 arXiv
[68]

Hamann, S

J. Hamann, S. Hannestad, G. G. Raffelt and Y. Y. Y. Wong, Observational bounds on the cosmic radiation density, JCAP 08 (2007) 021, [ 0705.0440]

2007 arXiv
[69]

Shun and P

Z. Shun and P. McCullagh, Laplace approximation of high dimensional integrals , Journal of the Royal Statistical Society: Series B (Methodological) 57 (12, 2018) 749–760

2018
[70]

Herold, E

L. Herold, E. G. M. Ferreira and L. Heinrich, Profile likelihoods in cosmology: When, why, and how illustrated with ΛCDM, massive neutrinos, and dark energy , Phys. Rev. D 111 (2025) 083504, [2408.07700]

2025 arXiv
[71]

Karwal, Y

T. Karwal, Y. Patel, A. Bartlett, V. Poulin, T. L. Smith and D. N. Pfeffer, Procoli: Profiles of cosmological likelihoods, 2401.14225

arXiv
[72]

E. B. Holm, L. Herold, T. Simon, E. G. M. Ferreira, S. Hannestad, V. Poulin et al., Bayesian and frequentist investigation of prior effects in EFT of LSS analyses of full-shape BOSS and eBOSS data , Phys. Rev. D 108 (2023) 123514, [ 2309.04468]

2023 arXiv
[73]

Nygaard, E

A. Nygaard, E. B. Holm, S. Hannestad and T. Tram, Fast and effortless computation of profile likelihoods using CONNECT , JCAP 11 (2023) 064, [ 2308.06379]

2023 arXiv
[74]

Yeche, A

C. Yeche, A. Ealet, A. Refregier, C. Tao, A. Tilquin, J. M. Virey et al., Prospects for dark energy evolution: A Frequentist multi-probe approach , Astron. Astrophys. 448 (2006) 831, [astro-ph/0507170]. 38

2006 arXiv
[75]

O’Shaughnessy, B

R. O’Shaughnessy, B. Farr, E. Ochsner, H.-S. Cho, C. Kim and C.-H. Lee, Parameter estimation of gravitational waves from nonprecessing black hole-neutron star inspirals with higher harmonics: Comparing Markov-chain Monte Carlo posteriors to an effective Fisher matrix , Phys. R...

2014 arXiv
[76]

Biscoveanu, C

S. Biscoveanu, C. Talbot and S. Vitale, The effect of spin mismodelling on gravitational-wave measurements of the binary neutron star mass distribution , Mon. Not. Roy. Astron. Soc. 511 (2022) 4350–4359, [2111.13619]

2022 arXiv
[77]

Olsen, J

S. Olsen, J. Roulet, H. S. Chia, L. Dai, T. Venumadhav, B. Zackay et al., Mapping the likelihood of GW190521 with diverse mass and spin priors , Phys. Rev. D 104 (2021) 083036, [ 2106.13821]

2021 arXiv
[78]

R. E. Kass, L. Tierney and J. B. Kadane, The validity of posterior expansions based on laplace’s method, Bayesian and Likelihood Methods in Statistics and Econometrics 7 (1997) 473 – 488

1997
[79]

A. N. Taylor and T. D. Kitching, Analytic Methods for Cosmological Likelihoods , Mon. Not. Roy. Astron. Soc. 408 (2010) 865, [ 1003.1136]

2010 arXiv
[80]

S. L. Bridle, R. Crittenden, A. Melchiorri, M. P. Hobson, R. Kneissl and A. N. Lasenby, Analytic marginalization over CMB calibration and beam uncertainty , Mon. Not. Roy. Astron. Soc. 335 (2002) 1193, [astro-ph/0112114]. 39

2002 arXiv

Pith tools

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

[1] [1]

Reeves, P

A. Reeves, P. Zhang and H. Zheng, PyBird-JAX: Accelerated inference in large-scale structure with model-independent emulation of one-loop galaxy power spectra , - (2025)

work page 2025

[2] [2]

B. L. Welch and H. W. Peers, On formulae for confidence points based on integrals of weighted likelihoods, Journal of the Royal Statistical Society. Series B (Methodological) 25 (1963) 318–329

work page 1963

[3] [3]

H. W. Peers, On confidence points and bayesian probability points in the case of several parameters , Journal of the Royal Statistical Society: Series B (Methodological) 27 (12, 2018) 9–16

work page 2018

[4] [4]

N. Reid, R. Mukerjee and D. A. S. Fraser, Some aspects of matching priors , Lecture Notes-Monograph Series 42 (2003) 31–43

work page 2003

[5] [5]

J. O. Berger, J. M. Bernardo and D. Sun, The formal definition of reference priors , The Annals of Statistics 37 (2009) 905 – 938

work page 2009

[6] [6]

D’Agostini, Bayesian reasoning in high-energy physics: Principles and applications , CERN Yellow Reports: Monographs (7, 1999)

G. D’Agostini, Bayesian reasoning in high-energy physics: Principles and applications , CERN Yellow Reports: Monographs (7, 1999)

work page 1999

[7] [7]

J. N. Fry and E. Gaztanaga, Biasing and hierarchical statistics in large scale structure , Astrophys. J. 413 (1993) 447–452, [ astro-ph/9302009]

arXiv 1993

[8] [8]

A. F. Heavens, S. Matarrese and L. Verde, The Nonlinear redshift-space power spectrum of galaxies , Mon. Not. Roy. Astron. Soc. 301 (1998) 797–808, [ astro-ph/9808016]. 12We thank Guido d’Amico for pointing to us this fact. 34

work page Pith review arXiv 1998