Calculate Posterior Probability of Flagged User Being Bad Actor

Q: Calculate Posterior Probability of Flagged User Being Bad Actor

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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Question

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.
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.

Calculate Posterior Probability of Flagged User Being Bad Actor

Bayesian inference for abuse detection with error control

Setup

Tasks

Solution

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