Bayes’ Rule and Sherlock Holmes 1/100 women at age forty who participate in a routine screening have breast cancer. 4:5 of women with breast cancer will get a positive mammography. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? In the BBC’s Sherlock Holmes, Mycroft Holmes mentions the ‘balance of probability’ several times. Bayes Rule is the rule that tells us how to balance two probabilities. The balance of two probabilities is sometimes *very counter-intuitive! Most people get the mammography problem wrong by a very large amount! The correct answer is ‘ . Holmes refers to ‘a simple deduction’; however, all the reasoning he explains are inductions. He *might* be referring to Bayes’ Rule which, in fact, was discovered with a very simple deduction. That said this point may be weak because it’s likely that Arthur Conan Doyle just confused the terms ‘induction’ and ‘deduction. Two statistics professors, Dr. Henle and Dr. Kanade, have scholarly articles in which the claim that Sherlock Holmes uses Bayesian Reasoning. One reason to think that they are right is the importance of Bayes’ Rule to doctors (the above problem for example) and Arthur Conan Doyle was trained as a Doctor about 100 years after the discovery of Bayes’ Rule. Bayes Rule is a formalized way of asking ‘How strong is the evidence that *disproves* what I believe?’ You can learn to be Bayesian in your everyday life by being aware of what you expected to find, looking for counter-examples to your beliefs and changing your degree of certainty in your beliefs based on your informal observations. As Dr. Daniel Kahneman said in Thinking, Fast and Slow, ‘not only can we be blind to the obvious but we can also be blind to our own blindness. For example, how many times do these players pass the basketballs between them: https://youtube/watch?v=IGQmdoK_ZfY
Posted on: Fri, 19 Sep 2014 19:40:50 +0000
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