Simulation-based cosmological inference from optically-selected galaxy clusters with $\texttt{Capish}$

Calum Murray; Constantin Payerne; Hugo Simon

arxiv: 2602.01911 · v3 · pith:KA7TLXSXnew · submitted 2026-02-02 · 🌌 astro-ph.CO

Simulation-based cosmological inference from optically-selected galaxy clusters with texttt{Capish}

Constantin Payerne , Calum Murray , Hugo Simon This is my paper

Pith reviewed 2026-05-25 06:44 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords simulation-based inferencegalaxy clusterscosmological parametersforward modelingnormalizing flowscluster abundanceweak lensing mass

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The pith

Capish applies simulation-based inference to forward-modelled galaxy cluster data for cosmological constraints.

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

The paper introduces Capish as a forward-modeling tool to simulate galaxy cluster catalogues including effects like selection functions and correlated scatter between richness and mass. It employs simulation-based inference using normalizing flows trained on abundance and lensing mass measurements to infer cosmological parameters. This avoids explicit likelihoods and captures more realistic systematics than analytic approaches. A reader would care because large upcoming surveys require precise control over biases to get accurate cosmology from cluster counts.

Core claim

Using Capish to generate forward-modelled catalogues and perform SBI with normalizing flows yields cosmological posteriors in good agreement with likelihood-based methods, but broader due to the increased realism of the forward model, and recovers parameters well when tested on catalogues from large cosmological simulations.

What carries the argument

Capish, the Python code that generates forward-modelled galaxy cluster catalogues from halo mass functions while incorporating observational effects, paired with neural density estimation via normalizing flows for SBI.

If this is right

Broader posteriors from SBI reflect more realistic treatment of systematics like selection biases and noise.
The method jointly models cluster abundance and mean lensing mass in redshift-richness bins.
Testing on simulation-built cluster catalogues shows good recovery of input cosmological parameters.
Applicable to large photometric surveys detecting hundreds of thousands of clusters.

Where Pith is reading between the lines

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

Extending Capish to include additional observables or more complex selection functions could further improve constraints.
Comparing results across different density estimators might reveal approximation errors in the normalizing flows.
This framework could be tested on real survey data from DES or LSST to validate against other cosmological probes.

Load-bearing premise

The forward model in Capish accurately captures all relevant observational systematics including the selection function, redshift uncertainties, and correlated scatter.

What would settle it

Observing a significant discrepancy between the SBI-inferred cosmological parameters and those from independent methods such as CMB measurements when applied to the same cluster catalogue would falsify the reliability of the forward model or the inference procedure.

read the original abstract

Galaxy clusters are powerful probes of the growth of cosmic structure through measurements of their abundance as a function of mass and redshift. Extracting precise cosmological constraints from cluster surveys is challenging, as we must contend the complex relationship between richness and the underlying halo mass, selection function biases, super-sample covariance, and correlated measurement noise between mass proxies. As upcoming photometric surveys are expected to detect tens to hundreds of thousands of galaxy clusters, controlling these systematics becomes essential. In this paper, we present a forward-modelling approach using Simulation-Based Inference (SBI), which provides a natural framework for jointly modelling cluster abundance and lensing mass observables while capturing systematic uncertainties at higher fidelity than analytic likelihood methods - which rely on simplifying assumptions such as fixed covariances and Gaussianity - without requiring an explicit likelihood formulation. We introduce $\texttt{Capish}$, a Python code for generating forward-modelled galaxy cluster catalogues using halo mass functions and incorporating observational effects. We perform SBI using neural density estimation with normalizing flows, trained on abundance and mean lensing mass measurements in observed redshift-richness bins. Our forward model accounts for realistic noise, redshift uncertainties, selection functions, and correlated scatter between lensing mass and observed richness. We find good agreement with likelihood-based analyses, with broader SBI posteriors reflecting the increased realism of the forward model. We also test $\texttt{Capish}$ on cluster catalogues built from a large cosmological simulation, finding a good fit to cosmological parameters.

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

Capish is a practical forward-modeling code for SBI on cluster abundance plus lensing, but the validation stays at the level of qualitative agreement.

read the letter

The paper's core contribution is Capish, a Python package that builds simulated cluster catalogs from halo mass functions, folds in selection functions, redshift scatter, and correlated noise between richness and lensing mass, then trains normalizing flows to do inference without an explicit likelihood. That setup is new for optically-selected samples and matches the needs of photometric surveys that will have hundreds of thousands of clusters. The authors show the SBI posteriors are wider than standard likelihood results, which is the expected outcome when the forward model carries more realistic systematics, and they recover input cosmology from a large simulation catalog. Those two checks are useful and directly address the stated goal. The main limitation is that the abstract and available description give no numbers on bias, coverage, or posterior width ratios, no training diagnostics for the flows, and no breakdown of which systematics drive the extra width. Without those, it is difficult to judge whether the forward model is accurate enough or whether the density estimator introduces its own bias. The work sits squarely in the cluster cosmology niche and will mainly interest people already running abundance-plus-lensing analyses who want a ready-made SBI pipeline. It is solid enough on its own terms to go to referees rather than desk reject, though the review will need to focus on the quantitative validation that is only sketched here.

Referee Report

1 major / 0 minor

Summary. The paper introduces Capish, a Python package for forward-modeling optically-selected galaxy cluster catalogs from halo mass functions while incorporating selection functions, redshift uncertainties, and correlated scatter between richness and lensing mass. It then performs simulation-based inference via normalizing flows trained on binned abundance and mean lensing-mass observables, claiming good agreement with conventional likelihood analyses (but with broader posteriors) and successful recovery of cosmological parameters when tested on catalogs drawn from a large cosmological simulation.

Significance. If the forward model and density estimator are shown to be unbiased, the approach would enable more realistic joint modeling of cluster abundance and weak-lensing mass proxies for upcoming photometric surveys, avoiding the Gaussianity and fixed-covariance assumptions of analytic likelihoods.

major comments (1)

[Abstract] Abstract: the statements 'We find good agreement with likelihood-based analyses' and 'finding a good fit to cosmological parameters' are made without any reported quantitative metrics (e.g., posterior overlap measures, bias values, or coverage probabilities), error budgets, or validation plots. This absence prevents assessment of whether the central claim—that SBI posteriors are unbiased and merely broader due to realism—actually holds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback. We address the single major comment below and will revise the manuscript to strengthen the presentation of results.

read point-by-point responses

Referee: [Abstract] Abstract: the statements 'We find good agreement with likelihood-based analyses' and 'finding a good fit to cosmological parameters' are made without any reported quantitative metrics (e.g., posterior overlap measures, bias values, or coverage probabilities), error budgets, or validation plots. This absence prevents assessment of whether the central claim—that SBI posteriors are unbiased and merely broader due to realism—actually holds.

Authors: We agree that the abstract statements would be strengthened by explicit quantitative metrics. The main text (Sections 4 and 5) presents visual comparisons of SBI and likelihood posteriors along with simulation-based recovery tests, but these are not summarized numerically in the abstract. In the revised manuscript we will update the abstract to report concrete metrics (e.g., posterior overlap integrals or mean parameter biases from the simulation tests) drawn directly from the existing figures and tables, and we will add a brief reference to the relevant validation plots. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central method is simulation-based inference (SBI) using normalizing flows trained on forward-modelled catalogues generated from external halo mass functions and large cosmological simulations. Validation consists of comparison to independent likelihood-based analyses and recovery tests on held-out simulation catalogues. No load-bearing self-citations, self-definitional equations, or fitted parameters re-presented as predictions are present. The approach is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are described in the abstract; the work relies on standard halo mass functions and external cosmological simulations.

pith-pipeline@v0.9.0 · 5792 in / 1018 out tokens · 20498 ms · 2026-05-25T06:44:19.271340+00:00 · methodology

discussion (0)

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