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Jonathan Bartlett, Director of Technology at New Medio argues, Distinguishing between types of probability can help us worry less and do more.
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| Portrait purportedly of Bayes used in a 1936 book,[1] but it is doubtful whether the portrait is actually of him.[2] No earlier portrait or claimed portrait survives. Photo: Wikipedia, the free encyclopedia |
Thomas Bayes (1702–1761) (pictured), a statistician and clergyman, developed a theory of decision-making which was only discussed after his death and only became important in the 20th century. It is now a significant topic in philosophy, in the form of Bayesian epistemology. Understanding Bayes’ Rule may be essential to making good decisions.
Let’s say that you are a generally healthy person and have no symptoms of any illness and no specific risk factors for any illness. Acting on a friend’s suggestion, you get screened for a variety of diseases, just to be sure. Of the diseases you test for, the HIV test comes back positive. You read on the package that the test is 99.6% accurate. Are you more likely to have the disease or not?...
If you are unsure about the calculations, think about it this way: Imagine that we are testing 1,000 people, pulled at random from the general population. Of those 1,000 people, only 1 person is statistically likely to have HIV. Let’s presume that, for that person, the test was accurate.
However, with a 99.6% accuracy rate, the test will fail four times out of a thousand. That means that we have, on average, four false positives in our sample of 1,000 people. Which means in turn that, of the five people who tested positive, only one person actually has the disease. This is slightly different from our calculation above because, as noted, we simplified it earlier for convenience of explanation. The actual calculated value is just about one out of four.
Source: Walter Bradley Center for Natural and Artificial Intelligence
