How I stop worrying about non-universality and $b_\phi$: Constraining local $f_{\rm NL}$ with $b_\phi$ priors from HOD posteriors

Jiaxi Yu; Nhat-Minh Nguyen

arxiv: 2607.01314 · v1 · pith:DRPL5UGBnew · submitted 2026-07-01 · 🌌 astro-ph.CO

How I stop worrying about non-universality and b_φ: Constraining local f_(rm NL) with b_φ priors from HOD posteriors

Jiaxi Yu , Nhat-Minh Nguyen This is my paper

Pith reviewed 2026-07-03 18:55 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords local primordial non-Gaussianityf_NLb_phihalo occupation distributionDESIgalaxy clusteringassembly bias

0 comments

The pith

Priors on b_phi derived from DESI HOD posteriors allow unbiased f_NL constraints on local primordial non-Gaussianity.

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

The paper addresses the dominant uncertainty in measuring local primordial non-Gaussianity by converting small-scale galaxy clustering data into priors on the response parameter b_phi. It fits a halo occupation distribution model to DESI Early Data Release clustering measurements, samples the resulting posterior, and generates mock catalogs to measure the distribution of b_phi values. These measurements supply the prior used in large-scale analyses. Validation tests on separate mock sets with injected local PNG signals confirm that the prior produces unbiased f_NL recovery, including cases that include assembly bias.

Core claim

Sampling the posterior of a halo occupation distribution model fit to DESI EDR small-scale clustering generates mocks from which b_phi is measured and its prior is constructed; validation against additional mocks with different local PNG amplitudes shows that the method recovers unbiased f_NL even in the presence of assembly bias.

What carries the argument

Sampling HOD posteriors fitted to small-scale clustering to measure and prior-constrain b_phi.

If this is right

The prior yields unbiased f_NL estimates from galaxy survey data.
The recovery remains unbiased when assembly bias is present.
The dominant uncertainty previously caused by unknown b_phi is reduced.
The same workflow can be repeated with data from other surveys or tracers.

Where Pith is reading between the lines

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

Small-scale clustering data can be repurposed to strengthen constraints on inflation parameters extracted from large-scale structure.
The approach reduces reliance on assumptions that b_phi takes a single universal value across galaxy samples.
Combining the resulting b_phi priors with multiple tracers could further tighten f_NL bounds in future analyses.

Load-bearing premise

The HOD posterior obtained from small-scale DESI EDR clustering fully captures the range of b_phi values realized by the actual galaxy population, including any effects of assembly bias.

What would settle it

A systematic offset between the recovered f_NL and the injected value in mocks whose assembly bias strength lies outside the variation spanned by the HOD posterior would falsify the claim.

Figures

Figures reproduced from arXiv: 2607.01314 by Jiaxi Yu, Nhat-Minh Nguyen.

**Figure 2.** Figure 2: FIG. 2. The 1D posterior of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: shows that lowering kmax to 0.08 h Mpc−1 recovers f true NL = −30 for LRG1 and LRG2, at the cost of ∼ 25% of the constraining power. We attribute the offset at the fiducial kmax to simulation systematics on mildly non-linear scales, not to a physical effect of negative fNL on the non-linear galaxy bias. 300 200 100 0 100 200 300 f loc NL 0.000 0.002 0.004 0.006 density fNL = 30 LRG1 300 200 100 0 100 200 3… view at source ↗

read the original abstract

Local primordial non-Gaussianity (local PNG) induces a scale-dependent contribution to galaxy clustering proportional to $f_{\rm NL}\,b_\phi$, where $f_{\rm NL}$ is the local PNG amplitude and $b_\phi$ encodes the galaxy response to a long-wavelength primordial potential perturbation. Uncertainty in $b_\phi$ is the dominant obstacle to precise, robust constraints on $f_{\rm NL}$ from galaxy surveys. We translate small-scale clustering constraints on the galaxy--halo connection into priors on $b_\phi$: sampling the posterior of a halo occupation distribution (HOD) model fit to the DESI EDR, we generate mocks from which we measure $b_\phi$ and construct its prior. Validating against additional mocks with different local PNG amplitudes, we show that the method recovers unbiased $f_{\rm NL}$, even in the presence of assembly bias.

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 workable recipe for building an empirical b_phi prior from an HOD fit to DESI EDR data and shows unbiased f_NL recovery inside that model family, but the validation does not test cases where real galaxies sit outside the HOD posterior.

read the letter

The core advance here is turning small-scale HOD constraints on DESI EDR into a data-driven prior on b_phi instead of relying on theoretical assumptions or fixed values. They sample the HOD posterior, generate mocks, measure b_phi on those mocks, and use the resulting distribution as the prior when fitting f_NL on large scales. The abstract reports that this recovers the input f_NL without bias even when assembly bias is included in the mocks.

That is useful in principle because b_phi uncertainty has been the main systematic holding back f_NL measurements. The approach is straightforward and directly tied to the same survey data that will be used for the f_NL analysis, which keeps the prior relevant.

The soft spot is exactly the one flagged in the stress test. The validation mocks are drawn from the identical HOD posterior used to build the prior, including the assembly-bias extensions that live inside that model. By construction, b_phi values in the test mocks fall inside the prior support. This means the test cannot reveal bias if the real galaxy population produces b_phi values the HOD posterior does not cover. No external simulation suite or independent galaxy-formation model is used to check that boundary.

The circularity is not total—the small-scale HOD fit and large-scale f_NL fit operate on different scales, and the prior is fixed before the f_NL step—but the robustness claim still rests on the assumption that the HOD posterior brackets reality. That assumption is stated but not stress-tested beyond the model family.

This is the kind of practical methods paper that people running f_NL analyses on DESI or Euclid will want to read. It deserves a serious referee to check the implementation details, the quantitative recovery numbers, and whether the prior construction can be made more conservative. I would send it to review rather than desk reject.

Referee Report

1 major / 1 minor

Summary. The paper claims that priors on the PNG response parameter b_φ can be constructed by sampling the posterior of an HOD model fit to small-scale DESI EDR clustering; mocks drawn from this posterior are then used both to measure the b_φ distribution and to validate that the resulting f_NL constraints remain unbiased even when assembly bias is included in the HOD.

Significance. If the central claim is correct, the approach supplies a data-driven route to marginalize over b_φ uncertainty that has been the dominant systematic in local f_NL analyses; it thereby converts existing small-scale clustering constraints into a practical prior for large-scale PNG measurements and could be directly applicable to full DESI and other Stage-IV surveys.

major comments (1)

[Validation section] Validation section (and abstract): the additional mocks used to demonstrate unbiased f_NL recovery are generated from the identical HOD posterior that supplies the b_φ prior. By construction, the b_φ values realized in these mocks lie inside the prior support; the test therefore cannot detect bias if the true galaxy population produces b_φ outside that support (e.g., from assembly-bias physics absent from the HOD model).

minor comments (1)

[Abstract] The abstract states that mocks recover unbiased f_NL but does not report the recovered values, uncertainties, or number of realizations; adding these quantitative results would strengthen the validation claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

Thank you for the referee's detailed review. We address the major comment on the validation section below.

read point-by-point responses

Referee: [Validation section] Validation section (and abstract): the additional mocks used to demonstrate unbiased f_NL recovery are generated from the identical HOD posterior that supplies the b_φ prior. By construction, the b_φ values realized in these mocks lie inside the prior support; the test therefore cannot detect bias if the true galaxy population produces b_φ outside that support (e.g., from assembly-bias physics absent from the HOD model).

Authors: We acknowledge that the validation procedure uses mocks generated from the same HOD posterior that defines the b_φ prior. Consequently, the test confirms unbiased f_NL recovery when the underlying galaxy population follows the HOD model constrained by the DESI EDR data, which incorporates assembly bias. It cannot, however, identify biases arising from b_φ values outside this support due to HOD model incompleteness. We will update the validation section to clarify this scope and emphasize that the prior is empirically derived from small-scale clustering observations. This approach still offers a practical way to incorporate b_φ uncertainty from data, and we note that extending the HOD model further would be a natural future direction. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained via scale separation

full rationale

The paper constructs a b_phi prior by fitting an HOD model to small-scale DESI EDR clustering, sampling the posterior to generate mocks, and measuring b_phi from those mocks before applying the prior to large-scale f_NL constraints. Validation proceeds by generating additional mocks with injected f_NL values from the same HOD posterior and recovering the input f_NL. No equations or steps reduce the final f_NL constraint to the HOD fit by construction; the small-scale vs. large-scale separation and the fact that the prior is fixed before the f_NL analysis keep the chain independent. No self-citations, ansatzes, or renamings are invoked in a load-bearing way that collapses the result to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the chosen HOD parametrization and the DESI EDR sample are representative of the b_phi distribution; no new physical entities are introduced.

free parameters (1)

HOD model parameters
Parameters of the halo occupation distribution are fitted to DESI EDR small-scale clustering to produce the posterior from which b_phi is sampled.

axioms (1)

domain assumption The halo occupation distribution model accurately describes the galaxy-halo connection properties relevant to b_phi on the scales used for the prior.
Invoked when mocks are generated from the HOD posterior and b_phi is measured in those mocks.

pith-pipeline@v0.9.1-grok · 5702 in / 1392 out tokens · 37178 ms · 2026-07-03T18:55:12.314063+00:00 · methodology

discussion (0)

Reference graph

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