##### Scenario Discussion on statistical foundations of a Bayesian spam-detection model already in production. ##### Question Compare prior, likelihood and posterior for a Beta-Binomial click-through model. Derive how the posterior mean acts as a smoothed estimate; when is it preferred to MLE? Explain how Bayesian credible intervals differ from frequentist confidence intervals in the context of model calibration. You observe concept drift; how would you update the prior or hierarchy to adapt more quickly? ##### Hints Use equations, reference conjugacy, and tie answers back to practical model monitoring.