# Research Question Selection

## Candidates considered

**A. Selection/completeness sensitivity of clustering measurements.**
Would require systematically varying completeness-correction schemes and comparing
resulting ξ(r)/P(k) — valuable but mostly reproduces well-established survey papers
without a novel angle for a solo project on a small footprint.

**B. Can ML-based systematics correction remove contamination without erasing true
large-scale structure?** Directly testable with injection studies on mocks with a
*known* truth, has clear falsifiable metrics (contamination removal vs. signal
distortion), and produces an honest negative-or-positive result either way. Matches
the depth of instruction in the project brief (injection studies, overcorrection
metrics, bias-variance frontier across model complexity, negative controls).

**C. Estimator stability for galaxy-environment measurements.** Interesting but is a
different measurement family (density/environment estimators, e.g. kNN, Voronoi) than
the clustering-statistics infrastructure the brief emphasizes; would fragment effort.

**D. Approximate/fast clustering computation.** A legitimate systems/performance
question, but orthogonal to the scientific systematics question, and lower scientific
payoff for the same engineering effort.

## Decision

**Primary question: B.**

> Do machine-learning correction methods (random forest / gradient-boosted trees) for
> observational/imaging systematics in a galaxy survey remove angular-density
> contamination more effectively than standard linear/weight-based correction, and — the
> question that actually matters — do they do so **without significantly distorting the
> true two-point clustering signal**, relative to an uncontaminated negative control?

Operationalized via:

1. A **real baseline measurement**: Landy-Szalay ξ(r) (or w(θ) if radial systematics
   dominate at the achievable sample size) on one public LRG/ELG/QSO tracer sample in
   one small sky region / one redshift bin, using the survey's own random catalog and
   weights.
2. A **controlled mock injection study** (the actual experiment): start from a mock
   with known clustering, inject documented-style systematics (depth/seeing/stellar
   density/extinction-like spatial templates), and compare correction methods:
   - no correction (contaminated baseline)
   - standard linear regression / weight-based correction (the survey-standard method)
   - ML correction (random forest, then gradient boosting) of increasing flexibility
   - **negative control**: apply every correction method to the *uncontaminated* mock
     and confirm it does not distort ξ(r) — this is the load-bearing test.
3. Metrics: contamination correlation reduction, fractional bias of corrected ξ(r)
   relative to true ξ(r), variance across mock realizations/seeds, and a
   bias-variance-style frontier across model complexity (Q42).

This is a **methodology/robustness** study. It does not attempt cosmological parameter
inference. If ML correction does not outperform the linear baseline once
signal-preservation is weighted in — a very plausible outcome — that negative result
is the reportable finding (per project's scientific-integrity mandate).

Subject to revision once data reconnaissance (`data_provenance.md`) confirms exactly
which tracer/release is used; the question and metrics above do not depend on that
choice.