[cailmdaley]

Claude (Opus) on behalf of Cail.

Where this fits. On the full UNIONS v2 area the ρ/τ PSF-leakage fit fails, with χ² 171/57. #452 diagnoses three causes:

• contaminated PSF stars, fixed by One catalogue-masking path for PSF stars and galaxies (manual-mask bit 8 via sky maps) #457 (merged);
• an estimator that ignores the noise in ρ: this PR;
• β growing with PSF size, still an open question in PSF-leakage fit fails on the full v2 area: three causes, and is β(T_PSF) physical? #452. This PR adds the model as an option, off by default.

Checking this PR against a known answer on mocks exposed a fourth problem: the template the fit uses for α doesn't match how leakage enters the galaxies. That is fixed upstream in CosmoStat/shear_psf_leakage#59 (closing #58 and #52) and adopted here.

Why change the estimator

The default lsq fit takes the measured ρ as exact and ignores the ρ–τ cross-covariance. At small θ, the noise in ρ propagated through the model is 100–500× the τ variance. So lsq's χ² and errors are wrong exactly where the fit has most weight. A joint errors-in-variables (EIV) fit handles this: it fits the true ρ alongside (α, β, η), under one jackknife covariance of ρ and τ together. #452 showed the cross-covariance term matters: dropping it fakes a pass, 69/57 instead of 78/57.

Why change α's template

The leakage model is e_gal += α·p_gal + β·(PSF error) + η·(size term), with τ the correlations of galaxy ellipticity with the star fields. The α column of the fit has been ρ, the PSF at stars, uncentred. Two things make that wrong:

• Centring: τ is built from galaxy ellipticities with their weighted mean removed, which also removes α times the mean PSF at the galaxies. ρ keeps its mean.
• Sampling: the leakage acts through the PSF at galaxy positions, not at stars.

α's column is now the PSF at galaxy positions, centred on the selected galaxies' weighted mean, correlated with the same star fields as τ. Its jackknife rows replace the old ones inside the joint covariance. ρ itself is unchanged, since it still feeds β, η and ξ_sys.

Known answer. We used two GLASS mocks painted on the real v2 catalogue that differ only by e += 0.1·p_gal:

α template	Δα (truth 0.1)
ρ at stars, uncentred (previous default)	0.080 ± 0.007
ρ at stars, centred	0.126 ± 0.007
centred PSF at galaxies (this PR)	0.0999999998

Through this PR's own measurement and fit, the full twin gives Δ(α, β, η) = (0.0999999998, −8×10⁻⁹, −2×10⁻⁸). Δτ matches 0.1 × the new α column to 10⁻¹³, in the full-sample vector and in every 200/400/800-patch jackknife row. The exact recovery is a consistency check: the twin difference is α times the centred galaxy PSF, so this shows the statistics and the fit now agree with the model; it doesn't test whether real leakage has that form. Each catalogue's own σ_α is 0.0053.

Not yet measured: the corrected fit on real v2 data. From the mock, the old template biased α low by about 20–25%, which is about 0.005 at α ≈ 0.02, below σ_α but systematic.

What changes

• rho_tau_method: eiv is the default.
  • Measurement: one TreeCorr pass measures ρ0–ρ5, τ0/τ2/τ5 and the α template on the same 800 star-derived patch centres.
  • Covariance: delete-one jackknife rows over all of them together. The 200- and 400-patch versions merge neighbouring patches (Ward clustering) without recounting pairs; 400 is the fiducial.
  • Fit: the noisy predictors are profiled out of a Hartlap-scaled χ² with the full predictor–τ cross-covariance.
  • Outputs: downstream code still receives Gaussian (α, β, η) samples. lsq and emcee remain selectable.
• β(T_PSF) = β₀ + β₁(T_PSF/⟨T_PSF⟩ − 1) is an option, off by default (psf_leakage.beta_psf_size). Its template is carried through the fit and ξ_sys.
• Caches. The rule cv_leakage_jackknife measures the joint products, and fitting and plotting read them. Every cached τ and leakage product records its field definition, columns, responses and selection, so a product made with the old full-catalogue centring can't be reused silently.
• Dependency. shear_psf_leakage is pinned to Cosmo val lisa #59's head (d0e10d83). It moves to the merge commit once Cosmo val lisa #59 merges.

Validation

• Against PSF-leakage fit fails on the full v2 area: three causes, and is β(T_PSF) physical? #452: with the old α column, the fit reproduces PSF-leakage fit fails on the full v2 area: three causes, and is β(T_PSF) physical? #452's own jackknife-row χ² to 10⁻¹², and its coefficients to 5×10⁻⁷σ. That figure uses the old α column, so it checks the estimator, not the new default:
  
• Tests cover:
  • coefficient recovery and the joint covariance;
  • replacement of α's column and rows;
  • selected-bin centring with unequal responses;
  • ξ_sys;
  • rejection of stale caches.
    Removing the α-row replacement or the τ provenance fails the corresponding test.
• Runs: the fast suite passes 697 tests, apart from six known site-specific failures on candide. Workflow DAG tests: 19 pass. CI is green on 7587907.

Limits.

• PTEs: absolute PTEs depend on the patch count and layout (PSF-leakage fit fails on the full v2 area: three causes, and is β(T_PSF) physical? #452's non-convergence); the coefficients and Δχ² don't.
• Scope of the mock test: it validates α's response only, not the PSF auto-power in ξ_sys or β/η.
• Cost: the full-area joint measurement took about 75 min and 83 GiB on 8 cores at bin_slop 0.1; the rule requests 128 GB and 4 h.

Refs #452

🤖 Generated with Claude Code

https://claude.ai/code/session_01JK7o9EG5R1yAPT98V9j2GJ