Change to Anderson-Darling for testing.

[mjlarson]

Using a chi2 fit to the CDF has always been a little gross and ugly. The chi2 isn't a great measure and it can lead to some parts of the distribution being overly important in the fit. A better choice would be to use something actually designed to run on CDFs instead. Here, I swap out the chi2 for an Anderson-Darling test, which seems to significantly improve the fits for the previously-worst bins. Most bins aren't affected here since they were fitting well anyway. Bias tests aren't showing much impact either, probably because most bins aren't changing.

Here's the worst bins from DNNCascades-ICEMAN along with their best-fits under chi2 (red) and AD (blue).

And the same for NorthernTracks v5.4

Note: this is branched off of mlarson/sigsub in #10 , so I have to merge that one first.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 86.04651% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.90%. Comparing base (981e816) to head (2f8ee83).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
kingmaker/utils.py	0.00%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #11      +/-   ##
==========================================
+ Coverage   78.87%   78.90%   +0.02%     
==========================================
  Files           6        6              
  Lines         923      948      +25     
==========================================
+ Hits          728      748      +20     
- Misses        195      200       +5     

Flag	Coverage Δ
test_basic	14.66% <11.62%> (+0.03%)	⬆️
test_fitting	37.76% <41.86%> (-0.38%)	⬇️
test_king_pdf	29.11% <55.81%> (+1.16%)	⬆️
test_template_smeared_king_pdf	25.84% <11.62%> (-0.27%)	⬇️
test_utils	16.24% <11.62%> (-0.01%)	⬇️
test_wrapper	38.81% <41.86%> (+0.35%)	⬆️

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[Copilot]

🔵 Needs a closer look

The scientific fitting objective and numerical interpolation changes warrant final domain-expert validation.

0 open findings

What changed in this PR

Replaces CDF chi-square fitting with an Anderson–Darling objective while incorporating RA-averaged signal-subtraction improvements from #10.

Changes:

• Adds the Anderson–Darling objective and analytical gradient.
• Improves RA-averaged PDF grids, validation, and interpolation.
• Expands numerical tests and updates signal-subtraction documentation.

File	Description
kingmaker/​fitting.py	Implements Anderson–Darling fitting.
kingmaker/​pdf.py	Improves marginalized PDF grids and validation.
kingmaker/​utils.py	Computes RA averages using adaptive grids.
kingmaker/​wrapper.py	Clarifies RA-averaged output semantics.
tests/​test_fitting.py	Tests the objective and gradient.
tests/​test_king_pdf.py	Tests normalization, accuracy, and clamping.
README.md	Updates signal-subtraction terminology.
docs/​signal_subtraction.rst	Documents RA averaging and grid behavior.
docs/​examples.rst	Updates examples and terminology.

🧠 Review effort: Balanced

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