The infinite hypothesis space problem

They say you’re supposed to choose your prior in advance. That's why it's called a “prior”. First, you’re supposed to say say how plausible different things are, and then you update your beliefs based on what you see in the world.

For example, currently you are—I assume—trying to decide if you should stop reading this post and do something else with your life. If you’ve read this blog before, then lurking somewhere in your mind is some prior for how often my posts are good. For the sake of argument, let's say you think 25% of my posts are funny and insightful and 75% are boring and worthless.

OK. But now here you are reading these words. If they seem bad/good, then that raises the odds that this particular post is worthless/non-worthless. For the sake of argument again, say you find these words mildly promising, meaning that a good post is 1.5× more likely than a worthless post to contain words with this level of quality.

If you combine those two assumptions, that implies that the probability that this particular post is good is 33.3%. That's true because the red rectangle below has half the area of the blue [...]

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Outline:

(03:28) Aliens

(07:06) More aliens

(09:28) Huh?

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First published:
December 18th, 2025

Source:
https://www.lesswrong.com/posts/JAA2cLFH7rLGNCeCo/good-if-make-prior-after-data-instead-of-before

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Narrated by TYPE III AUDIO.

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