Generalize Random feature defaults for greater stability

[odunbar]

Purpose

Closes #368

Content

• Removed learning of "sigma" which is not stably learnt!
• Applied some data standardization to ensure reasonable prior ranges, then chose some defaults that stay in this range
• Helped scale defaults with 1/sqrt(dimension) and 1/rank, for more general performance
• Allow for users to intentionally override overfit regularization (if over-regularization appears during optimization)
• Change default covariance regularization from "shrinkage" to "nice" (in ScalarRF)
• Changed (Corrected?) the "LR" factorization R*D*R' + eps*I to "LR plus D" R*R' + (D+eps)*I to rely less on the definiteness correction nugget eps
• Updated unit tests for latest EKP.
• We already can incorporate tikhonov with the prior distribution. therefore I have removed all mentions of other tikhonov regularization. the existing code was untested and not used anywhere.

MISC

• Added packages into Cloudy_emulate_sample that are missing.

Cloudy results (RF-scalar, RF-nonsep, gp-gpjl)

Regression 2d-2d results (true, RF-scalar, RF-nonsep, gp-skljl)

Plotting only 1st output component

L63 (RF-diag-scalar, RF-nonsep, gp-gpjl)

CDFs of long time trajectories (over 5 repeats for RF)

---

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

[codecov]

Codecov Report

❌ Patch coverage is 90.32258% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 93.61%. Comparing base (14e03ab) to head (1e0fca1).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/RandomFeature.jl	91.93%	5 Missing ⚠️
src/VectorRandomFeature.jl	86.11%	5 Missing ⚠️
src/ScalarRandomFeature.jl	92.30%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #375      +/-   ##
==========================================
+ Coverage   90.98%   93.61%   +2.62%     
==========================================
  Files          10       10              
  Lines        1609     1628      +19     
==========================================
+ Hits         1464     1524      +60     
+ Misses        145      104      -41     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[odunbar]

I am satisfied by the consistent examples/ stability improvements. Merging on successful tests and coverage.