Bayesian reasoning
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The design of organisations and products
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I could go on and on about the failings of Shakespeare ... but really I shouldn’t need to: the Bayesian priors are pretty damning. About half of the people born since 1600 have been born in the past 100 years, but it gets much worse than that. When Shakespeare wrote, almost all of Europeans were busy farming, and very few people attended university; few people were even literate—probably as low as about ten million people. By contrast, there are now upwards of a billion literate people in the Western sphere. What are the odds that the greatest writer would have been born in 1564?
- —Chauncey Gardiner’s “sophomore college blog”, quoted in Michael Lewis’ Going Infinite
You ever seen the dude from FTX? The one that went to prison? That dude shouldn’t be talking about Shakespeare.
- —Mike Tyson
Bayesian reasoning
beɪzˈiːən ˈpraɪə (n.)
A way to incorporate existing knowledge or beliefs about a parameter into statistical analysis. For example, if you believe that
- (a) all playwrights can be objectively ranked according to independent, observable criteria;
- (b) the quality of those playwrights in a given sample will be normally distributed;
and you think the best way of assessing the quality of dramas is by statistical analysis, then
- (i) you have already made several category errors, should not be talking about art, and if you are, no-one should be listening; but
- (ii) if, nonetheless, you are, and they are, and you are trying to estimate the statistical likelihood of a specific Elizabethan playwright being the best in history, then your knowledge that there were vastly fewer playwrights active in the Elizabethan period than have existed in all of history until now — which is a Bayesian prior distribution — might help you conclude that the odds of that Elizabethan playwright really being the best are vanishingly low.
At the same time, everyone else will conclude that you have no idea about aesthetics and a fairly shaky grasp even of Bayesian statistics.
Bayesian probabilities are a clever way of deducing, a priori, that we are all screwed. If you find yourself at or near the beginning of something, such as Civilisation, a bayesian model will tell you it will almost certainly end soon.
It works on elementary probability and can be illustrated simply.
Imagine there are two opaque barrels. One contains ten pool balls and the other contains ten thousand, in each case sequentially numbered from 1. You cannot tell which barrel is which.
A magician draws a ball with a seven on it from one barrel.
What are the odds that this came from the barrel with just ten balls?
Naive probability says that since both barrels contain a 7 ball, it is 50:50. Bayesian probability takes the additional fact we know about each barrel: the odds of drawing a seven from one barrel is 1 in 10, and from the other is 1 in 10,000, and concludes it is 1,000 times more likely that the 7 came from the barrel with just ten balls.
The proof of this intuition is if you drew ball 235, there would be no chance it came from the ten-ball barrel.
This logical reasoning is, obviously, sound. The same logic behind the “three door choice problem”
How do we get from this to the imminence of the apocalypse?
Well, the start of your life is, across the cosmic stretch of human existence, like a random draw with a sequentially numbered birth year on each ball.
Now imagine an array of one million hypothetical barrels containing balls engraved with sequentially numbered years, beginning at the dawn of civilisation which, for arguments sake, we shall call the fall of Troy.
The first barrel had just one ball, with the year in which Troy fell on it — the next has two:that year and the year after, and so on, up to one million years after the fall of Troy.
What are the odds that your birthday would be drawn at random from each one of those barrels? We know the odds for the first 6,000 or so: zero. But thereafter we can see that the probability steadily declines the more balls there are in the barrel.
Assessing the probability across all those million barrels is somewhat complicated but clearly the higher your birth year, the more probability there is that it resides in a higher barrel.