How to Update Bayesian Model for Concept Drift?

Q: How to Update Bayesian Model for Concept Drift?

This question evaluates a data scientist's understanding of Bayesian inference for binomial outcomes, including Beta–Binomial conjugate modeling, posterior estimation, credible intervals, and methods for adapting priors or hierarchies to handle concept drift.

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Question

Beta–Binomial CTR Model: Prior, Likelihood, Posterior, Smoothing, Intervals, and Drift

Context

You are discussing statistical foundations for a Bayesian spam-detection system already in production. For each unit (e.g., sender, campaign, or model bucket), you observe impressions and clicks and want a stable estimate of click-through rate (CTR) that supports monitoring and calibration.

Task

Specify the prior, likelihood, and posterior for a Beta–Binomial CTR model. Show the conjugate update.
Derive the posterior mean and show how it acts as a smoothed estimate. Compare to the MLE and state when the Bayesian estimate is preferred.
Explain how Bayesian credible intervals differ from frequentist confidence intervals, and how to use them for model calibration.
You observe concept drift. Propose how to update the prior or hierarchy so the model adapts more quickly, and tie your answer to practical monitoring.

How to Update Bayesian Model for Concept Drift?

Beta–Binomial CTR Model: Prior, Likelihood, Posterior, Smoothing, Intervals, and Drift

Context

Task

Solution

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