= 27d567bc2d48d9f40e9ccc20ea370b15)
Coscott comments on Open thread, July 21-27, 2014 - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (160)
Question about Bayesian updates.
Say Jane goes to get a cancer screening. 5% prior of having cancer, the machine has a success rate of 80% and a false positive rate of 9%. Jane gets a positive on the test and so she now has a ~30% chance of having cancer.
Jane goes to get a second opinion across the country. A second cancer screening (same success/false positive rates) says she doesn't have cancer. What is her probability for having cancer now?
Are we assuming the two tests are independent?
If so, the original cancer rate was 5:95. Multiply that by 80:9 for the likelihood ratio of getting a positive to get 400:855, which is ~30% as you said. Then, you multiply by the likelihood ratio of getting the second negative 20:91, to get 8000:77805, which as a probability is 8000/(8000+77805)~9.3%.