Thread by @doctorow

These are uncertain times, and uncertainty makes us anxious and sad. That's probably why the mathematics of uncertainty are so developed, and so important. It's the point behind #XKCD's brilliant "Garbage Math" strip/explainer:

pluralistic.net/2020/04/18/pol…

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The key to modeling uncertainty is Bayes's Theorem, which is also a subplot of my 2008 YA novel Little Brother. It's named after Thomas Bayes, the 18th century mathematician who is buried in Bunhill Cemetery, a beautiful and notorious plague pit near my old flat in London.

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Bayesian stats are key to all kinds of modern computing applications, including machine learning, which is interesting because they were kind of obscure for centuries and revived by electronic calculators, which make short work out of the tedious computation they demand.

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Writing in @GrantaMag, Morgan Agnew and David Peters do a superb job of explaining Bayesian reasoning as it applies to coronavirus testing. Antibody tests have four possible states: true negative, false negative, true positive and false positive.

granta.com/how-to-interpr…

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"The question we’d like to answer is: if you get a positive test, what is the probability you actually do have the antibodies you were tested for? Before we can get to a meaningful answer to that question though, we have to apply a certain amount of math and science."

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Your intuition about the answers will likely lead you astray. If a test is correct about positive 90% of the time, and correct about negative 80% of the time, then in a world where 10% of people are positive, your own positive test will be WRONG 66% of the time!

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"The real chance that a positive test is correct – 33% – is a lot lower than the percentages we were given for sensitivity and specificity. We need to do work to get from those figures to the answer — for an individual, what is the chance that a positive result is correct?"

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Frustratingly, getting the answer requires that we have a solid guess about what percentage of the population is infected - and we just don't know that. That's why it's so hard to be certain about anything else!

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Any time you see a report about a new covid test, check to see what the false positive AND false negative rates. Without those two figures, you can't really begin to understand whether the test will make a difference to our picture of the pandemic.

eof/