[audit-2026-07-09] Emulator-specific bugfixes from Audit.

[odunbar]

Purpose

• closes [audit 2026-07-09] General bugs for emulator interface and emulator-specific issues #451

Content

Emulators:

• Remove the safeguard "I" for deterministic maps, replace with 0
• rectified different emulators adding different "observational" noise on predictions - and centralize the addition of noise to outside of the predict(machine_learning_tool) call
• encoded noise is now stored- thus not assuming it must be I

GPs

• performance unification between different GP backends
• exact GP posterior Check tests
• warning if off-diagonal structure is present in covariances when it should not be
• remove some hard-coded Float64.
• rng for SKlearns optimizer
• remove the prediction type from GPs, (FINALLY!), and add deprecation notice

RFs:

• NICE correlation formula
• RF prior option was being ignored
• some docstring inconsistencies and outdated keywords
• guard if n_cov_samples < 2

Docs:

• consistency with the new prediction type API for GP, and not to internally add noise in mlt.
• a warning of deprecation for GP prediction type,
• also resolved some MCMC discrepancy

Examples:

• remove the GP prediction type

---

• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

❌ Patch coverage is 97.45763% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.92%. Comparing base (8368945) to head (00afcfd).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/MachineLearningTools/GaussianProcess.jl	95.65%	2 Missing ⚠️
src/MachineLearningTools/VectorRandomFeature.jl	92.85%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #453      +/-   ##
==========================================
+ Coverage   95.38%   95.92%   +0.53%     
==========================================
  Files          12       12              
  Lines        2537     2577      +40     
==========================================
+ Hits         2420     2472      +52     
+ Misses        117      105      -12     

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