Bayesian prior: Difference between revisions

Bayesian prior (view source)

Revision as of 09:08, 19 March 2024

2,258 bytes added , 19 March

no edit summary

Amwelladmin

Bureaucrats, Interface administrators, Administrators

82,503

edits

@@ Line 14: / Line 14: @@
 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.
 {{sa}}