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[ar1_bayes] Removed PyMC dependency and style-sheet compliance #569

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Key changes:

  • Removed PyMC: Removed all PyMC imports, installations, and model implementations
  • Updated variable naming: Used Greek letters (ρ, σ) instead of rho, sigma in NumPyro code
  • Code cleanup:
    • Cleaned up NumPyro implementation while preserving discussions
    • Fixed minor typos ("kernal" → "kernel")

@HumphreyYang HumphreyYang changed the title Removed PyMC dependency and style-sheet compliance [ar1_bayes] Removed PyMC dependency and style-sheet compliance Aug 22, 2025
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@github-actions github-actions bot temporarily deployed to pull request August 22, 2025 04:03 Inactive
@github-actions github-actions bot temporarily deployed to pull request August 22, 2025 04:03 Inactive
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