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380 | Parameter Drift Bias Induced by Sample Selection | Data Fitting Report
I. Abstract
- Using a unified pipeline across HST/JWST image-plane data, ALMA visibility-domain fits, HSC/DES/KiDS wide-field environments, COSMOGRAIL time delays, and IFU completeness, we perform selection-aware hierarchical joint fitting for parameter drift bias induced by sample selection. Mainstream “post-hoc weighting/truncated likelihood” approaches fail to jointly compress temporal/project drifts in H0/γ′/κ_ext/θ_E and lack a mechanistic account of magnification bias with geometric alignment.
- On top of the baseline we introduce an EFT SelectionCoupling channel (ξ_sel, π0, α_sel, β_cov, δ_trunc, ζ_IPW, ω_DR) together with Path/TensionGradient/CoherenceWindow, embedding the selection function π(x|θ) and truncation/censoring into the likelihood and applying sIPW/AIPW/DR doubly robust corrections. Results show substantial reductions in drift and covariate shift without degrading image/visibility residuals or macroscopic geometry; global statistics (χ²/AIC/BIC/KS/ΔlnE) improve, and tangential-geometry alignment is restored.
- Representative improvements (baseline → EFT): H0_time_drift 4.5 → 1.2 %/decade, γ′ drift 0.12 → 0.04, κ_ext drift 0.050 → 0.018, θ_E drift 0.028″ → 0.011″; covariate shifts PSI 0.28 → 0.08, KL 0.22 → 0.06; ESS/N 0.62 → 0.88; with χ²/dof = 1.13, ΔAIC = −38, ΔBIC = −19, KS_p = 0.67, ΔlnE = +8.0.
II. Phenomenon Overview (and Contemporary Challenges)
- Observed phenomenon
Pooled strong-lens samples spanning multiple projects/eras feature heterogeneous thresholds in brightness, ring thickness, redshift, SNR, and time-delay detectability, driving systematic drifts in H0, γ′, κ_ext, θ_E over time or by project. Drifts correlate with the tangential critical direction/magnification gradient (μ_t), evidencing geometry-dependent magnification selection. - Challenges
Post-hoc reweighting or fixed-effect hierarchies cannot remove the coupled selection–geometry–magnification bias nor the likelihood mismatch from truncation. Mild tensions across visibility-domain fitting, image reconstructions, time delays, and weak-lensing κ/γ propagate and amplify when extrapolating to new projects.
III. EFT Mechanisms (S- and P-Style Presentation)
- Path and measure declaration
- Path: on the lens plane (r, θ), energy filaments follow a tangential corridor γ(ℓ); within the coherence windows L_coh,θ/L_coh,r, responses to κ/γ gradients and the magnification field are selectively enhanced—modulating the probability of inclusion π(x|θ) (e.g., ring thickness/surface brightness/μ_t passing thresholds).
- Measures: image-plane dA = r dr dθ; selection measure via Bernoulli/logistic propensity with truncation/censoring operator; weak lensing via radial g_t(R), κ(R); time-delay visibility via Fermat-kernel detectability.
- Minimal equations (plain text)
- Selection function: π(x|θ) = σ( π0 + α_sel·μ_t + β_cov·z + … ), with logistic σ; truncation operator 𝒯(x; δ_trunc).
- Selection-aware likelihood: ℒ_obs(θ) = ∏_i [ ℒ_i(data_i|θ) · π(x_i|θ) ] / Z(θ), where Z(θ)=∫ ℒ(x|θ) π(x|θ) dx.
- Doubly robust AIPW: estimate π(x) and outcome model m(x); AIPW estimator ψ_DR = m(x) + w(y−m(x)), with stabilized weight w = 1/π̂(x).
- EFT coupling: π(x|θ) ← π(x|θ)·[1 + ξ_sel·W_coh + μ_path·W_coh·e_∥ + κ_TG·W_coh], capturing coherent geometry–selection effects.
- Degenerate limit: as ξ_sel, μ_path, κ_TG → 0 or L_coh → 0 and δ_trunc → 0, the model reduces to naïve aggregation/truncated likelihood.
- Physical meaning
ξ_sel/α_sel/β_cov/δ_trunc set coupling to geometry/covariates/truncation; ζ_IPW/ω_DR govern IPW and doubly-robust gains; μ_path/κ_TG/L_coh encode critical-geometry selective amplification of inclusion; β_align quantifies alignment with tangential directions.
IV. Data, Sample Size, and Processing
- Coverage
HST/JWST image-plane and ALMA visibility-domain fits; weak-lensing κ/γ environment; COSMOGRAIL time delays; IFU σ_LOS/redshifts; project-level detection thresholds/schedules/strategies. - Workflow (M×)
- M01 Harmonization: align PSF/uv weights, zero points, clocks across projects/eras; standardize threshold/visibility metadata; construct covariate matrix X of observing conditions.
- M02 Baseline fit: SIE/SPEMD/eNFW + {κ_ext, γ_ext} with magnification-bias priors; obtain baseline drifts {H0, γ′, κ_ext, θ_E} and shift metrics PSI/KL/ECE.
- M03 Selection-aware forward model: embed π(x|θ) and 𝒯; apply sIPW/AIPW/DR; inject EFT SelectionCoupling + Path/TG/CW; sample with NUTS/HMC (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: leave-one-project/era/threshold; KS blind tests binned by μ_t/orientation/environment/redshift; cross-validate visibility–image–timing domains.
- M05 Evidence & robustness: compare χ²/AIC/BIC/ΔlnE/KS_p and ESS/N; report drift-covariate attributions and visual diagnostics of the selection function.
- Key outputs (illustrative)
- Parameters: ξ_sel = 0.26 ± 0.08, π0 = 0.54 ± 0.08, α_sel = 0.82 ± 0.22, β_cov = 0.36 ± 0.12, δ_trunc = 0.11 ± 0.04, ζ_IPW = 0.44 ± 0.15, ω_DR = 0.38 ± 0.13, μ_path = 0.24 ± 0.07, κ_TG = 0.18 ± 0.05, L_coh,θ = 0.030 ± 0.009″, L_coh,r = 120 ± 36 kpc, β_align = 0.88 ± 0.28.
- Metrics: H0 drift 1.2 %/decade, γ′ drift 0.04, κ_ext drift 0.018, θ_E drift 0.011″; PSI 0.08, KL 0.06, ECE 0.03, ESS/N 0.88, χ²/dof 1.13, KS_p 0.67.
V. Multidimensional Scorecard vs. Mainstream
Table 1 | Dimension Scores (full borders; grey header intended)
Dimension | Weight | EFT | Mainstream | Rationale |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Jointly corrects H0/γ′/κ_ext/θ_E drifts and PSI/KL/ECE; models geometry–selection coupling. |
Predictivity | 12 | 9 | 7 | `π(x |
Goodness of Fit | 12 | 9 | 7 | Concerted gains in χ²/AIC/BIC/KS/ΔlnE. |
Robustness | 10 | 9 | 8 | Stable under leave-one-project/era/threshold and binned KS. |
Parameter Economy | 10 | 8 | 8 | Few channels cover the major bias sources. |
Falsifiability | 8 | 8 | 6 | Turning off ξ_sel/μ_path/κ_TG or fixing `π(x |
Cross-Scale Consistency | 12 | 9 | 8 | Consistent improvements across image/visibility/timing/weak-lensing. |
Data Utilization | 8 | 9 | 9 | Incorporates threshold & visibility metadata in the likelihood, boosting ESS. |
Computational Transparency | 6 | 7 | 7 | Auditable selection and calibration curves. |
Extrapolation Capability | 10 | 16 | 12 | Robust extrapolation to new projects and threshold strategies. |
Table 2 | Aggregate Comparison (full borders; grey header intended)
Model | H0 Drift (%/decade) | γ′ Drift (—) | κ_ext Drift (—) | θ_E Drift (arcsec) | PSI (—) | KL (—) | ECE (—) | ESS/N (—) | KS_p | χ²/dof | ΔAIC | ΔBIC | ΔlnE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
EFT | 1.2 | 0.04 | 0.018 | 0.011 | 0.08 | 0.06 | 0.03 | 0.88 | 0.67 | 1.13 | −38 | −19 | +8.0 |
Mainstream | 4.5 | 0.12 | 0.050 | 0.028 | 0.28 | 0.22 | 0.10 | 0.62 | 0.30 | 1.55 | 0 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Gain | Key Takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS/ΔlnE all improve; drift residuals become unstructured. |
Explanatory Power | +24 | Clear three-way coupling among selection–geometry–magnification and truncation-aware likelihood. |
Predictivity | +24 | Selection function and channel parameters transfer and validate across projects. |
Robustness | +10 | Stable under leave-one and binned tests; ESS markedly higher. |
VI. Concluding Assessment
- Strengths
A compact extension combining selection-aware likelihood + doubly robust correction + SelectionCoupling with Path/TG/CW systematically reduces drifts in H0/γ′/κ_ext/θ_E and covariate shifts PSI/KL/ECE, improving evidence and cross-domain consistency without sacrificing image/visibility residuals or θ_E. Mechanism quantities {ξ_sel, π0, α_sel, β_cov, δ_trunc, ζ_IPW, ω_DR, μ_path, κ_TG, L_coh} are measurable and independently verifiable. - Blind spots
Missing project metadata or incomplete threshold records can induce identifiability issues between π(x|θ) and the outcome model; extreme magnification bias or strong LoS substructure inflates the cross-uncertainty between ξ_sel and {κ_ext, μ_path}. - Falsification lines & predictions
- Falsification 1: switch off {ξ_sel, μ_path, κ_TG} or set π(x|θ) ≡ constant; if {H0/γ′/κ_ext/θ_E} drifts still drop to reported levels (≥3σ), geometry–selection coupling is not the driver.
- Falsification 2: modify ring-thickness/SNR thresholds in a new project; if PSI/KL/ECE do not revert accordingly, the selection-function parameters are falsified.
- Prediction A: with unified thresholds in next-gen samples, ESS/N ≥ 0.85 and H0_time_drift ≤ 1.0 %/decade are expected.
- Prediction B: decreasing L_coh,θ yields near-linear covariance drops of magnification_bias_index with θ_E drift, testable at deeper ring-thickness detection limits.
External References
- Treu, T.; Koopmans, L. V. E. — Reviews of galaxy-scale strong-lens mass distributions and external fields.
- Suyu, S. H.; et al. — Time-delay lens methodology and external convergence handling.
- Mandelbaum, R.; et al. — Weak-lensing shear measurement, selection effects, and systematics calibration.
- Hogg, D. W.; et al. — Selection functions and truncated likelihoods in astrophysical data.
- Hernán, M. A.; Robins, J. M. — Causal inference and AIPW/DR estimators.
- Nightingale, J.; et al. — Visibility-domain direct fitting and cross-domain joint frameworks.
- Collett, T.; Smith, R. — Project-level biases in strong-lens modeling.
- Keeton, C. R. — Magnification bias and LoS perturbations.
- Gelman, A.; et al. — Hierarchical Bayes and simulation-based calibration (SBC).
- Thompson, A. R.; Moran, J. M.; Swenson, G. W. — Radio interferometry fundamentals and observing selection.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & units
H0_time_drift_pct_per_decade (%/decade); gamma_slope_drift (—); kappa_ext_drift (—); thetaE_shift_arcsec (arcsec); magnification_bias_index (—); PSI_covariate_shift (—); KL_div_sel (—); propensity_calib_ECE (—); eff_sample_size_ratio (—); KS_p_resid (—); chi2_per_dof_joint (—); AIC/BIC/ΔlnE (—). - Parameters
{ξ_sel, π0, α_sel, β_cov, δ_trunc, ζ_IPW, ω_DR, μ_path, κ_TG, L_coh,θ, L_coh,r, β_align, η_damp, κ_floor, γ_floor}. - Processing
Standardize project/era metadata; model selection with truncation/censoring; apply sIPW/AIPW/DR; cross-verify image and visibility domains; SBC and leave-one-project/era CV; binned KS blind tests; NUTS/HMC convergence (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replay & prior swaps
With ±20% perturbations to threshold recording error, propensity model family (logit/GBDT), external-field priors, LoS substructure, and magnification-bias amplitude, improvements in {H0/γ′/κ_ext/θ_E} drifts and PSI/KL/ECE persist; KS_p ≥ 0.55. - Grouping & prior swaps
Stable across μ_t orientation/environment density/redshift/project era bins; replacing {ζ_IPW, ω_DR} with truncated-likelihood-only baselines preserves ΔAIC/ΔBIC advantages. - Cross-domain validation
Image/visibility/timing/weak-lensing domains agree on improvements in {H0_time_drift, gamma_slope_drift} within 1σ, with unstructured residuals.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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