A Bayesian estimator for peculiar velocity correction in cosmological inference from supernovae data

Shiv K. Sethi; Tarun Deep Saini; Ujjwal Upadhyay

arxiv: 2502.09258 · v4 · submitted 2025-02-13 · 🌌 astro-ph.CO

A Bayesian estimator for peculiar velocity correction in cosmological inference from supernovae data

Ujjwal Upadhyay , Tarun Deep Saini , Shiv K. Sethi This is my paper

Pith reviewed 2026-05-23 03:32 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords peculiar velocitysupernova cosmologyBayesian estimationerrors-in-variablesmagnitude-redshift relationcosmological parametersPantheon samplenon-linear models

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The pith

Bayesian estimator corrects for peculiar velocities while fitting supernova cosmology models, without assuming linearity or Gaussian velocities.

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

Peculiar motions of supernova host galaxies bias cosmological parameter estimates from magnitude-redshift data. Conventional fixes either reconstruct velocity fields assuming a background cosmology or inflate magnitude errors under linear and Gaussian approximations. The paper develops a Bayesian estimator that fits the cosmological model and corrects for both coherent and random peculiar velocities at the same time by recasting the magnitude-redshift relation as a non-linear errors-in-variables problem. A general fitting procedure for such models is derived, then specialized and validated on simulations matching current and upcoming survey precision before application to the Pantheon sample. The approach supplies an alternative that needs no independent velocity measurements and extends to other errors-in-variables tasks in cosmology and astronomy.

Core claim

The paper presents a Bayesian estimator that simultaneously corrects for peculiar motion and fits a cosmological model to supernova data by treating the magnitude-redshift relation as a non-linear model with errors in both variables, relaxing the usual linearity and Gaussianity assumptions on the velocity corrections.

What carries the argument

Bayesian estimator for non-linear errors-in-variables models, specialized to the magnitude-redshift relation.

If this is right

Cosmological inference from supernovae proceeds without separate velocity-field reconstructions that presuppose a cosmology.
Random peculiar-velocity contributions are treated without requiring linear magnitude-redshift approximations or Gaussian velocity distributions.
The method supplies a complementary route for the coherent velocity component that does not need independent velocity measurements.
The same errors-in-variables machinery applies directly to other cosmological and astronomical fitting problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The estimator could be inserted into existing supernova analysis pipelines to check consistency of parameters obtained under the older linear-Gaussian assumptions.
For future wide-field surveys the joint fitting may reduce the need for auxiliary velocity reconstructions when mapping local flows.
The general method opens a route to propagate non-Gaussian velocity tails into distance-ladder or standard-siren analyses that also involve redshift-dependent errors.

Load-bearing premise

The general non-linear errors-in-variables fitting method can be specialized to the magnitude-redshift relation and validated at survey precision without biases from prior choice or velocity distribution treatment.

What would settle it

Application of the estimator to simulated supernova catalogs at Pantheon-level precision recovers input cosmological parameters with no systematic offset when realistic peculiar velocities are injected.

Figures

Figures reproduced from arXiv: 2502.09258 by Shiv K. Sethi, Tarun Deep Saini, Ujjwal Upadhyay.

**Figure 1.** Figure 1: Constraints on the ΛCDM parameters from synthetic data with magnitude error 𝜎𝑚 = 0.2 (left) and 𝜎𝑚 = 0.05 (right). Estimator E1 (red) ignores any contribution to redshift from the peculiar motion of supernovae host galaxies, E2 (blue) considers it for the linearized model (see Appendix A for details), while E3 (green) represents our estimator, which incorporates the contribution from peculiar motion for th… view at source ↗

**Figure 2.** Figure 2: Constraints on the 𝑤CDM parameters from synthetic data with 𝜎𝑚 = 0.2 (left) and 𝜎𝑚 = 0.05 (right). The colour scheme of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of different estimators with only a random peculiar motion. The colour scheme of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of different estimators with only the coherent component of peculiar motion. The colour scheme of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: The figure shows posterior distributions and credible regions of ΛCDM parameters from Pantheon data using three different estimators. It follows the convention used in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: The figure shows posterior distributions and credible regions of 𝑤CDM parameters from Pantheon data using three different estimators. It follows the convention used in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

read the original abstract

The peculiar motion of the host galaxies introduces bias in estimating cosmological parameters from supernova data. The coherent component of the peculiar motion is usually corrected for using velocity field reconstruction based on the observed galaxy distribution, while the random component is treated statistically by inflating the magnitude uncertainty in the quadrature derived using the standard error propagation. The method of velocity field reconstruction requires assuming an underlying cosmology, which can introduce its own bias in the final inference. On the other hand, the statistical treatment of the random component assumes a locally linear approximation for the magnitude-redshift relation and a Gaussian distribution for the peculiar velocities, which can have extended tails in the non-linear regime. In this work, we present a Bayesian estimator for simultaneously correcting for peculiar motion while fitting a cosmological model to the supernova data, relaxing the assumption of linearity of the model and Gaussianity of the random peculiar motion. Our approach is based on considering the problem of fitting the magnitude-redshift relation as a non-linear model with errors in both dependent and independent variables. To this end, we develop a general method for fitting such non-linear errors-in-variables models. We then specialize it to the case of fitting the magnitude-redshift relation, validating it with simulated datasets at the precision of current and upcoming surveys, and testing it on the Pantheon sample. Our method provides an alternative approach for accounting for the peculiar velocity effects, which is a complementary method for the coherent component, as it does not require independent velocity measurements, and generalizes the treatment of the random component. Moreover, our general method is applicable to various other problems in cosmology and astronomy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a Bayesian errors-in-variables treatment that folds peculiar-velocity corrections into the cosmology fit itself, avoiding external velocity reconstructions that assume a model.

read the letter

The main thing here is a general Bayesian method for non-linear errors-in-variables regression, then specialized to the supernova magnitude-redshift relation so that peculiar velocities are handled inside the fit rather than corrected beforehand. That removes the need for a cosmology-dependent velocity-field reconstruction for the coherent part and drops the usual linear-plus-Gaussian assumptions for the random part. They run it on simulated data at current and next-generation survey precision and also apply it to Pantheon. That is the concrete advance: a self-contained statistical treatment that can be used as a complement or alternative to the standard pipeline. The validation on mocks is the part that actually matters for whether the method holds up at the precision level claimed. The soft spots are modest. The abstract does not show the size of the bias reduction or the posterior shifts on dark-energy parameters, so the practical payoff still needs to be checked in the numbers. Prior choices in the Bayesian setup are not discussed in detail here, and any sensitivity there would show up in the full results. The general EIV machinery looks reusable beyond this problem, which is a plus. This is for people doing supernova cosmology or similar distance-ladder work who want to test whether their velocity handling is introducing model dependence. It is not a headline result but a useful methodological option with explicit validation steps. I would send it to a serious referee; the core construction is clear enough and the tests are the right kind to evaluate.

Referee Report

1 major / 2 minor

Summary. The paper presents a Bayesian estimator for simultaneously correcting for peculiar motion while fitting a cosmological model to supernova data. It frames the magnitude-redshift relation as a non-linear errors-in-variables model, develops a general method for fitting such models, specializes the approach to supernovae (relaxing linearity and Gaussianity assumptions), validates it on simulated datasets at current and upcoming survey precision, and tests it on the Pantheon sample. The method is positioned as complementary to velocity-field reconstruction since it requires no independent velocity measurements.

Significance. If the derivation and validation hold, the work supplies a useful alternative for peculiar-velocity handling in supernova cosmology that avoids the cosmology dependence of reconstruction methods and generalizes the statistical treatment of the random component. The general non-linear EIV fitting procedure is a potential strength with applicability to other problems in cosmology and astronomy. Explicit validation on both simulations and real data is a positive feature.

major comments (1)

[Validation on simulated datasets] The central claim that the method introduces no biases from the choice of priors or velocity-distribution treatment (weakest assumption) requires explicit sensitivity tests in the validation on simulated datasets; without quantitative demonstration that posterior cosmological parameters remain stable under reasonable prior variations, the assertion of unbiased recovery at survey precision is not fully supported.

minor comments (2)

The abstract states that the approach 'relaxes the assumption of linearity... and Gaussianity' but does not quantify the resulting change in parameter uncertainties or bias relative to the standard quadrature inflation method.
[Method section] Notation for the joint posterior and the treatment of the velocity distribution in the specialized magnitude-redshift case should be cross-referenced to the general EIV equations for clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and recommendation of minor revision. We address the major comment below.

read point-by-point responses

Referee: [Validation on simulated datasets] The central claim that the method introduces no biases from the choice of priors or velocity-distribution treatment (weakest assumption) requires explicit sensitivity tests in the validation on simulated datasets; without quantitative demonstration that posterior cosmological parameters remain stable under reasonable prior variations, the assertion of unbiased recovery at survey precision is not fully supported.

Authors: We agree that explicit sensitivity tests would strengthen the validation section. In the revised manuscript we will add quantitative tests on the simulated datasets, varying the prior on the velocity dispersion parameter and considering non-Gaussian forms (e.g., Student-t with heavier tails) for the random peculiar-velocity component. We will report the resulting shifts in the recovered cosmological parameters and demonstrate stability within the reported posterior uncertainties at both current and Stage-IV survey precision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained methodological development

full rationale

The paper develops a general Bayesian method for non-linear errors-in-variables regression, then specializes it to the supernova magnitude-redshift relation for simultaneous peculiar-velocity correction and cosmological fitting. This is validated on simulated data at survey precision and tested on Pantheon; the approach relies on standard Bayesian inference and errors-in-variables techniques without reducing any central result to a fitted input, self-citation chain, or definitional equivalence. No load-bearing step in the provided description collapses by construction to the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into specific parameters or assumptions; the central approach rests on treating magnitude and redshift as having errors in both variables and on the applicability of the general non-linear fitting method to cosmology.

axioms (1)

domain assumption The magnitude-redshift relation can be treated as a non-linear model with measurement errors in both variables.
This is the explicit modeling choice that enables the Bayesian estimator described in the abstract.

pith-pipeline@v0.9.0 · 5825 in / 1166 out tokens · 36401 ms · 2026-05-23T03:32:53.638395+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages · 1 internal anchor

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DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

Abdalla E., et al., 2022, JHEAp, 34, 49 Abdul Karim M., et al., 2025, arXiv e-prints: 2503.14738 Abell P. A., et al., 2009, arXiv:0912.0201 Adame A. G., et al., 2024, arXiv: 2411.12022 Aghanim N., et al., 2018, Astron. Astrophys., 617, A48 Aghanim N., et al., 2020, Astron. Astrophys., 641, A6 Brout D., et al., 2022, Astrophys. J., 938, 110 Carr A., Davis ...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/c2017-0- 2022

[1] [1]

DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

Abdalla E., et al., 2022, JHEAp, 34, 49 Abdul Karim M., et al., 2025, arXiv e-prints: 2503.14738 Abell P. A., et al., 2009, arXiv:0912.0201 Adame A. G., et al., 2024, arXiv: 2411.12022 Aghanim N., et al., 2018, Astron. Astrophys., 617, A48 Aghanim N., et al., 2020, Astron. Astrophys., 641, A6 Brout D., et al., 2022, Astrophys. J., 938, 110 Carr A., Davis ...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/c2017-0- 2022