How to Update Bayesian Model for Concept Drift?
Overview
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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Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
62
0
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.
Solution
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