Compute posterior spam risk from flags

Q: Compute posterior spam risk from flags

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Question

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.

Compute posterior spam risk from flags

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