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Compute posterior spam risk from flags
This question evaluates understanding of Bayes' theorem, conditional probability, and interpretation of classifier performance metrics (true positive and false positive rates) for computing posterior spam risk.
A binary classifier flags spammy requesters. Last week the base rate of spam among all requesters was 12%. The classifier has true positive rate (TPR) 0.90 and false positive rate (FPR) 0.04.
a) Using Bayes' theorem, compute P(Spam | Flagged). Show your formula and final numeric answer rounded to 4 decimals. b) Compute P(Spam | Not Flagged) and interpret it (what fraction of unflagged requesters are still spam?). c) If the base rate dropped to 6% with the same TPR/FPR, recompute P(Spam | Flagged). Briefly explain how base rate changes affect the posterior and why.
Provide all steps, formulas, and final answers.
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