= 27d567bc2d48d9f40e9ccc20ea370b15)
buybuydandavis comments on What's wrong with this picture? - Less Wrong Discussion
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 (80)
It's no more probable under the null hypothesis, but much more probable under more probable than average alternative hypotheses.
Such as gods interfering with our lives?
Imagine, for a moment, you've ruled out all of the probable explanations. Are you still going to be looking for an alternative explanation, or will you accept that it's chance?
Or the coin being cheat, or some cheating or "non-random" effect in the situation. Delusional recollection of events.
How did I "rule out" the alternatives? When I imagine me doing that, I imagine me reasoning poorly. I go by Jaynes' policy of having a catch all "something I don't understand" hypothesis for multiple hypothesis testing. In this case, it would be "some agent action I can't detect or don't understand the mechanism of". How did I rule that out?
Suppose it's 1,000,000 coin flips, all heads. The probability of that is pretty damn low, and much much lower than my estimates for the alternatives, including the "something else" hypothesis. You can make some of that up with a sampling argument about all the "coin flip alternatives" one sees in a day, but that only takes you so far.
I don't see how I would ever be confident that 1,000,000 came up all heads with "fair" coin flipping.
It's a fair coin. It just has two heads on it.
The probability of any specific sequence of 1M coin flips is "pretty damn low" in the same sense. The relevant thing here is not that that probability is low when they're all heads, but that the probability of some varieties of "something else" is very large, relative to that low probability. Or, more precisely, what sets us thinking of "something else" hypotheses is some (unknown) heuristic that tells us that it looks like the probability of "something else" should be much bigger than the probability of chance.
(I guess the heuristic looks for excessive predictability. As a special case it will tend to notice things like regular repetition and copies of other sequences you're familiar with.)