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Calculate Posterior Probability of Flagged User Being Bad Actor

MetaData Scientist · Onsite
EasyData ScientistOnsiteStatistics & Math

Last updated

Evaluates Bayesian inference and confusion-matrix reasoning for abuse detection. Strong answers derive posterior precision from prevalence, TPR, and FPR, define Type I and Type II errors, and compute true positives and false positives for 10 million users.

Scenario

Platform must distinguish good users from potential bad actors using Bayesian inference while controlling error rates.

Question

Given a prior probability p of a user being a bad actor and classifier outputs with known true-positive and false-positive rates, derive the posterior probability that a flagged user is truly bad. Define Type I and Type II errors in this context and explain their business impact. If 1 % of 10 million users are truly bad and the classifier has 95 % recall and 2 % false-positive rate, calculate the expected number of bad actors caught and the expected number of good users incorrectly flagged.

Hints

Apply Bayes’ theorem, build a 2×2 confusion matrix, compute expected counts from prevalence and error rates.