The Formula of Thomas Bayes and Other Matters
There is a blood test for the HIV virus causing AIDS. This test is quite good in the sense that if an individual has the virus the probability of detection is high. How is such a probability estimated? As we have mentioned before, the Law of Large Numbers soon to be discussed justifies our intuitive notion that a probability can be estimated by considering relative frequencies. So in this case we can give the test to a large population where we know the disease, and therefore the virus, is present. If the test is positive for, say, 95 percent of this population, we can say that.95 is a rough estimate for what is called the sensitivity of the test, defined as P(test ispositive/disease is present).
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