Help with Bayesian Inference?
You go to the health center where both Doctor A and Doctor B independently (i.e. you have separate appointments with each of them) consider the possibility that you have cogscitis, a brain condition caused by a virus.
Doctor A gives the hypothesis that you do have cogscitis a prior probability of 0.70 (so, the prior probability of the not-cogscitis hypothesis is 0.3). Doctor B gives the cogscitis hypothesis a prior probability of 0.20.
The doctors each order three tests, and the results come back sequentially: the results of test 1 come back first, the results of test 2 come back second, and the test 3 results come back third. The Doctors both engage in Bayesian updating after seeing the results of each test.
Hypothesis // Probability of positive test result given hypothesis
not cogscitis 0.10
After getting the results from Test 1, what is Doctor A's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.
It's the problem I need help with. Sorry if it was confusing.
- AmyLv 73 weeks agoFavorite Answer
Was the result of test 1 positive or negative?
probability of cogscitis given positive test result = (prior probability of cogscitis and positive test) / (prior probability of positive test)
prior probability of cogscitis and positive test = prior probability of cogscitis * probability of positive test given cogscitis
prior probability of positive test = prior probability of cogscitis and positive test + prior probability of not cogscitis and positive test
- DixonLv 73 weeks ago
Is the penultimate paragraph what you meant to put? I don't understand its grammar or meaning.