Quadratic estimators for CMB weak lensing
Bibliographic record
Abstract
In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from the observed CMB temperature $T$ and polarization $E$ and $B$ fields. Until very recently, this reconstruction has been performed with quadratic estimators (QEs), which, although known to be suboptimal for high-sensitivity experiments, are numerically efficient and useful to make forecasts and cross-check the results of more sophisticated likelihood-based methods. It is expected that ongoing and near-future CMB experiments, such as AdvACT, SPT-3G, and the Simons Observatory (SO), will also rely on QEs. In this work, we review different QEs and clarify and quantify their differences. In particular, we show that the Hu-Okamoto (HO02) estimator is not the absolute optimal lensing estimator that can be constructed out of quadratic combinations of $T$, $E$, and $B$ fields. Instead, we derive the global-minimum-variance (GMV) lensing quadratic estimator. Although this estimator can be found elsewhere in the literature, it was erroneously described as equivalent to the HO02 estimator and has never been used in real data analyses. Here, we show explicitly that the HO02 estimator is suboptimal to the GMV estimator, with a reconstruction noise larger by up to $\ensuremath{\sim}9%$ for a SO-like experiment. We further show that the QE used in the Planck and recent SPT lensing analysis are suboptimal to both the HO02 and GMV estimator and would have a reconstruction noise up to $\ensuremath{\sim}11%$ larger than that of the GMV estimator for a SO-like experiment. In addition to clarifying differences between different QEs, this work should thus provide motivation to implement the GMV estimator in future lensing analyses relying on QEs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".