Compute posterior spam risk from flags
Company: Snapchat
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
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.
Quick Answer: 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.