Transcription of 3 Basics of Bayesian Statistics - Carnegie Mellon University
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3 Basics of Bayesian Statistics - Carnegie Mellon University
3 Basics of Bayesian StatisticsSuppose a woman believes she may be pregnant after a single sexual encounter,but she is unsure. So, she takes a pregnancy test that is known to be 90%accurate meaning it gives positive results to positive cases 90% of the time and the test produces a positive , she would like to know theprobability she is pregnant, given a positive test (p(preg|test +)); however,what she knows is the probability of obtaining a positive test resultif she ispregnant (p(test +|preg)), and she knows the result of the a similar type of problem, suppose a 30-year-old man has a positiveblood test for a prostate cancer marker (PSA). Assume this test is alsoap-proximately 90% accurate. Once again, in this situation, the individualwouldlike to know the probability that he has prostate cancer, given the positivetest, but the information at hand is simply the probability of testingpositiveif he has prostate cancer, coupled with the knowledge that he tested Theorem offers a way to reverse conditional probabilities and,hence, provides a way to answer these questions.
In this chapter, I first show how Bayes’ Theorem can be applied to answer these questions, but then I expand the discussion to show how the theorem can be applied to probability ... ( p= .85) (see Exercises). If the woman is aware of the test’s limitations, she may choose to repeat the
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