Week 5 · Suggested 75 minutes · First-pass draft
Rare events and the base-rate trap
Compare what a classifier promises with what a positive result actually means, then connect counts to Poisson assumptions.
Applied assignment, not a stored grade. Instructions and model checks are provided for self-study or instructor adaptation. Work is not transmitted to this site.
What you will do
- Use prevalence 1%, sensitivity 90%, and specificity 95% to calculate positive predictive value by hand.
- Check the result with the Bayesian base-rate lab and then increase prevalence while keeping the test properties fixed.
- For a Poisson count with mean two, calculate the probability of zero events.
- Write two cautions about applying either simple probability model to actual observational evidence.
What to submit
A 2-by-2 expected-count table, the conditional probability calculation, Poisson result, and limitations paragraph.
Self-check before finishing
The predictive value is about 15.4%; a Poisson(2) variable has P(X=0) ≈ .1353.
Assigned reading
Use Bayes, expected values, binomial and Poisson models.
- Lesson 15: bayes and base rates
- Lesson 16: expected value and variance
- Lesson 17: random variables and binomial
- Lesson 18: poisson and rare events
Instructor discussion guidance
Watch for students who mistake sensitivity for predictive value or describe the fictional test as clinical guidance.
Print a predict–experiment–explain worksheet → · Open browser R →