Linguistics 696 - Statistical Methods in Computational Linguistics
Assignment #1
Bayes' Rule
Let's imagine we have a contagious disease and a test for the disease. The facts are the following:
- Among people who have the disease, 100% of the time the test correctly classifies the patient as positive for
the disease.
- Among people who do not have the disease, 95% of the time the test correctly classifies the patient as
negative for the disease, 5% of the time it is incorrect (false positive).
- 1% of the population has the disease.
Our question is a policy question. Do we quarantine people who have a positive test result? For your work, use the following labels.
- T is the size of the total population.
- D is the set of people who have the disease.
- H is the set of people who are healthy (do not have the disease).
- P is the set of people who TEST positive for the disease.
- N is the set of people who TEST negative for the disease.
Assume the following are true:
- T = D + H
- T = P + N
We base our decision on:
P(D|P)
Compute this quantity using Bayes' Rule. Show your work.
Make a recommendation regarding quarantining.
Textbook Exercises
Exercises 2.5, 2.7 (p. 60); 2.9. (pp. 78,79)
Extra Credit
Exercise 2.13(p. 79).