Posted: January 23rd, 2020
Bayes Homework in 3 hours
Assessment Brief
Objectives
· Experiment
with independence
· Use
Bayes law in small problems.
· See how
Bayes law can be used to solve (somewhat) real problems.
Bayes Homework [10
points] This problem comes from G. Gigerenzer, "Calculated Risks: How To
Know When Numbers Deceive You", Simon and Schuster Press, 2002. Give the
answer and show how you obtain the results using Bayes rule.
To
diagnose colorectal cancer, the hemoccult test --- among others --- is
conducted to detect occult blood in the stool. This test is used from a
particular age on, but also in routine screening for early detection of
colorectal cancer. Imagine you conduct a screening using a hemoccult test in a
certain region. For symptom-free people over 50 years old who participate in
screening using the hemoccult test, the following information is available for
this region.
The
probability that one of these people has colorectal cancer is 0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that this person
will have a positive hemoccult test. If a person does not have colorectal
cancer, the probability is 3 percent that this person will still have a
positive hemoccult test. Imagine a person (over age 50, no symptoms) who has a
positive hemoccult test in your screening. What is the probability that this
person actually has colorectal cancer.
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