= 27d567bc2d48d9f40e9ccc20ea370b15)
Vladimir_Nesov comments on The prior of a hypothesis does not depend on its complexity - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (59)
In other words, universal prior assigns probability to points, not events. Probability of an event is sum over its elements, which is not related to the complexity of the event specification (and hypotheses are usually events, not points, especially in the context of Bayesian updating, which is why high-complexity hypotheses can have high probability according to universal prior).
For an explicit example of a high-complexity event with high prior, let one-element event S be one of very high Kolmogorov complexity, and therefore contain a single program that is assigned very low universal prior. Then, not-S is an event with about the same K-complexity as S, but which is assigned near-certain probability by universal prior (because it includes all possible programs, except for the one high-complexity program included in S).
Right.
The problem with your example is that 'not-S' is not an event, it's a huge set of events. It's like talking about the integer 452 and the 'integer' not-452.
The simplest beliefs about the events within that set can be extremely simple. For example, if S is described by the bits 1001001, the beliefs corresponding to non-S would be, "the first bit is 0', or "the second bit is 1", or, "the third bit is 1", and so forth.
Events aka hypotheses are sets of programs.
It's OK, the post itself was pretty stupid and I guess it was infectious. Here's my attempt to fix things.