broad

[RyanAugust]

Identified & Fixed Issues:

1. Tinygrad Syntax Errors: Corrected multiple instances of Tensor.traning (typo for Tensor.training). Also removed the non-existent with Tensor.train(): context manager, which is not supported in Tinygrad's API (it uses the global
   Tensor.training flag instead).
2. MCMC Numerical Stability: Improved the log_prior function in the Bayesian fit logic to explicitly return -inf if parameters become non-positive during sampling. This prevents NaN errors when calculating logarithms of negative numbers or
   zero.
3. Redundant Logic: Removed the unused format_currency_k function, as the currency formatting is now handled more efficiently via inline lambdas in the plotting logic.
4. Hill Function Verification: Verified the mathematical implementation of the Marginal ROAS (first derivative) and the Inflection Point (second derivative). Both were found to be mathematically sound.

Summary of Changes:

• Fixed typos in Tinygrad state management.
• Cleaned up invalid Tinygrad context managers.
• Hardened the MCMC sampler against invalid parameter proposals.
• Removed dead code.