Calculate Posterior Probability of Flagged User Being Bad Actor
Overview
This question evaluates understanding of Bayesian inference and classifier evaluation metrics, including Bayes' theorem, true/false positive rates, prevalence effects, and confusion-matrix reasoning for detection systems.
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Jul 12, 2025, 6:59 PM
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Bayesian inference for abuse detection with error control
Setup
A platform runs a binary classifier that flags users who might be bad actors. Let:
- p = prior probability a random user is a bad actor (prevalence)
- TPR (recall) = P(flag | bad)
- FPR = P(flag | good)
Tasks
- Derive the posterior probability that a flagged user is truly a bad actor, P(bad | flag), in terms of p, TPR, and FPR.
- Define Type I and Type II errors in this context and explain their business impact.
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If 1% of 10,000,000 users are truly bad, the classifier has 95% recall and 2% false-positive rate, compute:
- The expected number of bad actors caught (true positives).
- The expected number of good users incorrectly flagged (false positives).
Hints: Apply Bayes’ theorem, build a 2×2 confusion matrix, compute expected counts from prevalence and error rates.
Solution
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