Compute posterior for accurate-but-rare classifier
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
In a population, 5% are 'bad' users and 95% are 'good'. A screening model predicts 'bad' with sensitivity 0.95 (P(pred=bad | bad)=0.95) and specificity 0.95 (P(pred=good | good)=0.95). (a) If the model predicts 'bad' for a user, compute P(user is actually bad). (b) If the model predicts 'good', compute P(user is actually good). (c) Explain how these posteriors change with the prevalence and why this illustrates the base-rate effect.
Overview: This question evaluates understanding of Bayes' theorem and probabilistic reasoning for interpreting classifier outputs, specifically computing posterior probabilities given sensitivity, specificity, and prevalence.
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