Bayesian fit

[RyanAugust]

• Bayesian MCMC Engine: Added MarketingReturnCurve.fit_bayesian(), which utilizes a Metropolis-Hastings sampler to estimate the joint posterior distribution of the Hill Curve parameters (α, β, K).
• Prior Support: Users can now pass a priors dictionary (LogNormal parameters) to incorporate domain knowledge or results from previous models (e.g., Google Meridian).
• Posterior Access: A new posterior_samples attribute stores the full MCMC chains, allowing users to perform custom risk analysis or extract credible intervals.
• Probabilistic Predictions: Updated predict_incremental_return and predict_marginal_return with a use_samples=True flag to return a distribution of possible outcomes instead of a single point estimate.
• Uncertainty Visualization: Enhanced plot_response_curve to automatically render 90% credible intervals, providing a clear visual representation of model confidence.