Richard Ngo challenged me to set a time box and write down as many of the most important features of my formal epistemology as I can in one sitting. Here goes.

Where probability distributions fail...

...to express beliefs

There is no probability distribution over that says "". That is a support condition about probability distributions, namely, ⨾⨾. Some s satisfy this condition and some do not; but there is no that expresses the range belief itself.
There is no probability distribution over that says " and are independent". This is an equation condition about probability distributions, namely, . Some s satisfy this equation and some do not; there is no that expresses the independence belief itself.
There is no probability distribution over that can express a conditional probability distribution , even though this is just as essential a part of a Bayesian reasoner's epistemic state as her prior. A conditional probability distribution is a family of probability distributions indexed by the condition variable, not a probability distribution. There is no single distribution that expresses it.

...to make safety tradeoffs

Suppose there is an unfair coin, which you know to be unfair (but not exactly how much or [...]

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Outline:

(00:21) Where probability distributions fail...

(00:25) ...to express beliefs

(01:26) ...to make safety tradeoffs

(02:17) Beliefs, according to davidad

(03:06) All other known notions of belief fit in nicely

(03:11) Bayesian beliefs

(03:21) Bayesian updating

(05:05) Infra-Bayesian beliefs (Kosoy and Appel)

(06:01) MWER (Halpern and Leung)

(06:45) Probabilistic dependency graphs (Richardson and Halpern)

(07:25) Credal sets (Cozman)

(07:52) Previsions (Goubault-Larrecq)

(08:40) The monad (Mio, Sarkis, and Vignudelli)

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First published:
July 29th, 2026

Source:
https://www.lesswrong.com/posts/e7Pd4Q9TF7jFdmPgz/imprecise-beliefs-a-tiny-introduction

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Narrated by TYPE III AUDIO.

“Imprecise beliefs: a tiny introduction” by davidad

LessWrong (30+ Karma)

“Imprecise beliefs: a tiny introduction” by davidad