Bayesian Reasoning
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Another way of thinking of at least some uses of it is to take an answer to the wrong question and turn it into an answer to the question you actually want an answer to. This often comes up with medical testing, where you can have a test that’s very accurate but most of the positive results are false.
Say you have a test for Zoidberg’s Disease that’s 95% accurate. This is the answer to the wrong question — that means that if you have Zoidberg’s Disease, there’s a 95% chance that the test will be positive, and if you don’t have it, there’s a 95% chance the test will be negative. This isn’t any help to you, the patient, because if you knew you have Zoidberg’s Disease you wouldn’t go getting a test for it. What you want to know is: my test came back positive, what does that mean for me? And the answer will depend on how common Zoidberg’s Disease is.
Let’s say it’s rare, only 2% of people have it. So in our city of 100,000 people:
98000 don’t gots it
2000 gots it
And our test is 95% accurate, so:
* 95% of the 98000, or 91300, don’t gots it and get a negative result
* 4900 out of the 98000 don’t gots it but get a positive result
* 95% of the 2000, or 1900, gots it and get a positive result
* 100 of the 2000 gots it and get a negative result
Put that together, and how many people get a positive result? 6800. But only 1900 of them actually have Zoidberg’s Disease, so only 28% of positive results are correct even though 95% of total test outcomes are correct.
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