No-one’s going to read this reply, as I’m 13 years too late, but—oh dear me—MacKay makes hard work of the medical example.
A straightforward Frequentist solution follows. There are 4 positive cases among the 30 subjects in class A and 10 subjects in class B. We’ll believe that treatment A is better if it’s very unlikely that, were the treatments identical, there would be so relatively few positive cases among the A’s. There are 91390 ways of picking 4 from 40, with only 3810 ~= 4.17% having 0 or 1 in class A. So, unless we were unlucky (4.17% chance) with the data, we can conclude that treatment A is better.
Paul Gowder,
You’ve read Jaynes—now read MacKay.
“Information Theory, Inference, and Learning Algorithms” (available for download here).
The key portions are sections 37.2 − 37.3 (pp 462-465).
No-one’s going to read this reply, as I’m 13 years too late, but—oh dear me—MacKay makes hard work of the medical example.
A straightforward Frequentist solution follows. There are 4 positive cases among the 30 subjects in class A and 10 subjects in class B. We’ll believe that treatment A is better if it’s very unlikely that, were the treatments identical, there would be so relatively few positive cases among the A’s. There are 91390 ways of picking 4 from 40, with only 3810 ~= 4.17% having 0 or 1 in class A. So, unless we were unlucky (4.17% chance) with the data, we can conclude that treatment A is better.