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3 Basics of Bayesian Statistics

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.

50 3 Basics of Bayesian Statistics 3.2 Bayes’ Theorem applied to probability distributions Bayes’ theorem, and indeed, its repeated application in cases such as the ex-

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