[cailmdaley]

Summary

Goal: one definition of the galaxy weights, the metacal shear response R = R_shear + R_sel, the image-sim residual multiplicative bias m and the additive bias c, used end to end on data and image sims. One knob, metacal.weight_scheme: des | iv, sets all four.

Findings:

• The response follows Martin's DES-weight definition ("case d"). With his settings, the code reproduces his R, weight table and paired m on all 20 sim products to 10⁻¹⁴.
• Paired m is inconsistent with that response. m is now measured on full populations, which lowers it by ~1.5 percentage points (pp).
• A weight table fitted on the galaxies it weights biases m low. The sims now use a fixed table fitted on v2 data.
• The production residual is m = (−9.2 ± 3.2, −8.9 ± 3.6) × 10⁻³, about −1%. It is concentrated at low SNR and not explained.
  • Its shear-response part is (−15.8, −17.8) × 10⁻³. The selection part offsets it by (+6.6, +8.9) × 10⁻³.
  • Martin's check, with no SNR/size cuts and no weights (so R_sel ≡ 0), gives m = (−32 ± 4, −22 ± 4) × 10⁻³. That is not zero.
  • No fiducial m is adopted.
• On v2 data, R rises by 10.6% (0.643 → 0.712), almost entirely from the weighting.

Figures are hosted on the orphan branch pr-assets/425, outside the PR's history. Definitions: docs/source/response_calibration.md. Reproduction: scripts/validation/response/README.md.

Terms

Term	Meaning
Metacal branches	Each galaxy is remeasured after an artificial shear ±h (h = 0.01) along component j = 1, 2, giving branches b ∈ {ns, 1+, 1−, 2+, 2−}; ns is the unsheared (no-shear) measurement, and e_b is the ellipticity measured on branch b.
R_shear	(⟨e_{j+}⟩ − ⟨e_{j−}⟩) / 2h on the no-shear selection and weights: how the measured shape responds to shear. R = R_shear + R_sel calibrates g = R⁻¹e.
Branch mean	⟨x⟩_b = Σ w_b x / Σ w_b, over metacal branch b's own selection S_b and with its own weights w_b. Each branch has its own denominator, so R is the derivative of the same weighted ratio it calibrates.
Split R_sel (applied)	(⟨e_ns⟩{j+} − ⟨e_ns⟩{j−}) / 2h. The no-shear ellipticity is averaged with each sheared branch's selection and weights. This captures cut crossings, weight changes and cell migration.
Joint R (diagnostic)	(⟨e_{j+}⟩{j+} − ⟨e{j−}⟩_{j−}) / 2h, using each branch's own ellipticity.
Case d	Fit the DES weight table W(SNR, T/T_psf) once on the no-shear branch, then evaluate it at each branch's own SNR and size. This is Martin's wdes_response.py.
IV weights	1/(2σ_ε² + σ₁² + σ₂²): σ_ε is the per-component intrinsic shape dispersion, σ₁, σ₂ each branch's own measured G_ERR.
c	c_e = ⟨e⟩_ns raw, c_g = R⁻¹c_e calibrated, and g = R⁻¹e − c_g.
Paired m	Match the +g and −g sim objects that pass the cuts in both, and give each pair the weight ½(w₊ + w₋). This was Martin's estimator.
Full-population m	Each external-shear catalogue keeps its own selection, weights and R. This is now the production estimator.
The gap	Paired m minus full-population m.
Self-weighting	A table fitted on the galaxies it weights correlates W with their shapes. In a noiseless toy, this gives m = −1/N_cell; an independent table gives 0.
N_min	Minimum number of no-shear training objects per DES cell. A cell below 3 pools moments over the smallest surrounding square of cells that reaches 3. Denser cells are unchanged.
Shared-tile jackknife	Delete-one-tile errors. Each deletion removes the same tile from both external-shear catalogues and recomputes R and the numerator.
Refit-W errors	For a self-fitted table, each deletion also refits W, so the errors carry the table's noise. An independent table stays fixed.

What the PR contains

• Library: branch-normalised R, case-d DES and exact per-branch IV weights, and c in explicit units.
  • The producer and the cosmo_val consumer read the same components.
  • Products record their weight scheme and applied R in their headers. Readers refuse a mismatched weight or a second R.
• Image-sim m:
  • Full populations only. Modern products refuse pair_match: true.
  • The DES table is a named, independent product, held fixed across branches and deletions. des_weight_source: self remains as a diagnostic.
  • Errors use the shared-tile jackknife, with full (m1, c1, m2, c2) covariance.
• Tests for each rule, including the self-weighting toy. Fast suite: 586 passed, 0 failed.
• Martin's image-sims workflow is also merged here: the workflow/bin/spv launcher, workflow/scripts/status_sims.py, the image-sims Snakefile/config, and his Global shear response is IV-weighted while shear statistics are w_des-weighted #395 reference scripts in scripts/validation/wdes_response/.

Results

All four unblinded grids are combined as inverse-variance means, assuming the grids are independent. m is given as (m1, m2) × 10⁻³.

Estimator

• The gap, ~1.5 pp.
  • Paired m combines to (−4, 0). With the same self-fitted table, full populations give (−19.3 ± 4.0, −14.3 ± 4.7).
  • Symmetric pair weights drop the weight change from the numerator, but case-d R keeps it.
  • Matched objects with separate branch weights already show most of the gap, so it comes mostly from the weights; restricting the population contributes less.
• Self-weighting, ~0.5–1 pp.
  • Training on the other three grids gives (−11.2 ± 3.3, −8.1 ± 3.9).
  • The v2 data table, which is the production rule, gives (−9.2 ± 3.2, −8.9 ± 3.6).
  • Paired m (self-fitted table) minus full-population m with the other-grids table is ~0.7 pp. That's a cross-table difference, not the gap measured with one independent table.
• Exact IV: (−16.1 ± 4.1, −17.0 ± 4.7).
  • No fitted table, so self-weighting can't explain it. Freezing the no-shear G_ERR would shift m by +0.2 to +0.4 pp. Modern IV therefore refuses inputs that lack the sheared G_ERR columns.
• N_min = 3. Without it, one two-object cell inflated a grid's σ(m) fivefold. Errors plateau over N_min = 3–10; m moves ≤ 0.21σ.

m split into shear-response and selection parts

m_shear-only calibrates with R_shear alone. δm_sel is the change from adding R_sel, at fixed numerator and population, so m = m_shear-only + δm_sel. Grids are combined with the total-m weights so the split stays additive.

Configuration	m_shear-only	δm_sel	m
No SNR/size cuts, unit weights	(−32.1 ± 3.8, −21.7 ± 3.6)	0	(−32.1 ± 3.8, −21.7 ± 3.6)
SNR/size cuts, unit weights	(+12.8 ± 4.2, +14.3 ± 4.1)	(−29.4 ± 4.4, −31.5 ± 4.9)	(−16.6 ± 4.3, −17.2 ± 4.9)
SNR/size cuts, DES (production)	(−15.8 ± 3.1, −17.8 ± 3.2)	(+6.6 ± 3.2, +8.9 ± 3.8)	(−9.2 ± 3.2, −8.9 ± 3.6)

Martin's check (top row). Every retained object passes all five branch masks, so R_sel is exactly zero.

• What it shows: m is still 8σ and 6σ from zero, so R_shear alone does not calibrate these sims.
• What it doesn't show: it does not place the bias in shape measurement. The parent cuts (FLAGS ≤ 2, N_EPOCH ≥ 2, 15 ≤ mag ≤ 30, ngmix failure flags) and detection/blending still act, and none of them enters R.

Under production cuts and weights, the negative residual sits in the shear-response part, and the selection part partly cancels it. Changing cuts or weights also changes the numerator, so comparing rows is not a physical split into measurement bias and selection bias.

Open: a −1% residual, concentrated at low SNR

The terciles are set by the v2 data's SNR distribution.

• By tercile: m1 is (−39 ± 25, −24 ± 11, −2 ± 4), and m2 is similar. High minus low is 1.3–1.6σ.
• Occupancy: the sims hold ~30% fewer galaxies than the data at SNR 10–15, and the per-galaxy response climbs from ≈0.4 to ≈0.8 over SNR 10–30. Reweighting the sims to the data's SNR × size occupancy gives (−11.9 ± 3.5, −10.4 ± 4.2).
• Response at fixed SNR: data galaxies below SNR 40 also respond less than sim galaxies at the same SNR, as if noisier than nominal (inferred). If so, the sims understate the low-SNR bias.
• Not tested: detection and blending, and the non-metacal parent cuts.

A release's m must be measured with that release's own table.

v2 data: what catalogue users feel

Global calibration of v2 data at d604206, with #424 (halo masks dropped):

	old	this PR
R_shear (diag)	0.641, 0.643	0.734, 0.735
R_sel (diag)	+0.002, +0.002	−0.022, −0.022
R total (diag)	0.643, 0.645	0.711, 0.713
c_e (×10⁻⁴)	(−0.6, +0.7)	(−0.1, +1.8) ± 0.3

• Old calibration: an IV-weighted R_shear (unsquared errors) combined with an unweighted R_sel.
• Source of the shift: weighting accounts for 99.6% of it; Default external-mask cut excludes the star halos #424 leaves R unchanged.
• Mechanism: DES weights favour high-response galaxies. R_shear is 0.602 unweighted, 0.610 with IV², and 0.734 with DES.
• Effect: calibrated shear falls by 9.6% (1/1.106), and ξ by ~18%.

Follow-ups

• ShapePipe should keep the eight sheared G_ERR columns in its merge allow-list. Without them, IV mode can't run on merged catalogues.
• m-bias errors: leave-one-tile-out jackknife; drop the cumulative file #346: the tile jackknife is delivered; mbias_cumulative.yaml and plot_convergence remain.
• Calibration: scalar shear response across estimators, object-wise PSF leakage #382: only the additive-bias units are fixed here.
• shear two-point calibration response #23: the shear-only scale dependence of R on the data is ≤ 0.1% (ξ± shifts ≤ 0.014σ per bin); selection/weight derivatives remain.
• Still open: the low-SNR residual, and the v2 null-test PTEs with this calibration.

Closes #395, Closes #156, Closes #21, Closes #22. Refs #23, #346, #382.

Claude (Opus) on behalf of Cail

🤖 Generated with Claude Code

[github-actions]

✅ ruff is clean — nothing to fix here.