Compute posterior for accurate-but-rare classifier

Q: Compute posterior for accurate-but-rare classifier

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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Question

Bayes' Theorem: Interpreting Screening Model Predictions

Context

You are evaluating a binary screening model that flags "bad" users in a population. The model has known sensitivity and specificity, and the population has a known prevalence of "bad" users.

Prevalence: P(bad) = 5%, P(good) = 95%.
Sensitivity: P(pred = bad | bad) = 0.95.
Specificity: P(pred = good | good) = 0.95 (so false positive rate = 0.05).

Tasks

(a) If the model predicts "bad" for a user, compute P(user is actually bad).

(b) If the model predicts "good" for a user, compute P(user is actually good).

(c) Explain how these posterior probabilities change with the prevalence and why this illustrates the base-rate effect.

Compute posterior for accurate-but-rare classifier

Bayes' Theorem: Interpreting Screening Model Predictions

Context

Tasks

Solution

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Compute posterior for accurate-but-rare classifier

Overview

Bayes' Theorem: Interpreting Screening Model Predictions

Context

Tasks

Solution

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