Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

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

cogscitis 0.70

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.

Thanks!

Update:

It's the problem I need help with. Sorry if it was confusing.

2 Answers

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  • Amy
    Lv 7
    3 weeks ago
    Favorite 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 

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  • Dixon
    Lv 7
    3 weeks ago

    Is the penultimate paragraph what you meant to put? I don't understand its grammar or meaning. 

    • Dixon
      Lv 7
      3 weeks agoReport

      Rather than vote this down, why not answer the OP if you know what it means.

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