Negative probability thread! (it's the tweet version of this blog post, as an experiment: https://drossbucket.wordpress.com/2019/08/01/negative-probability/ …)
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I'm not going to go too much into why people get interested in negative probabilities in the first place. For that (as for so many things) the best place to go is a blog post by
@johncarlosbaez:https://johncarlosbaez.wordpress.com/2013/07/19/negative-probabilities/ …1 reply 0 retweets 9 likesShow this thread -
Instead I'm going to go through an example that shows *how* they work. I got this one from another excellent blog post, by
@sigfpe: http://blog.sigfpe.com/2008/04/negative-probabilities.html … I like it because the numbers are nice and simple.1 reply 0 retweets 6 likesShow this thread -
So we have the following setup (from that post): "a machine produces boxes with (ordererd) pairs of bits in them, each bit viewable through its own door"
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Now we ask 3 questions: 1. Is the first box in state 0? 2. Is the second box in state 0? 3. Are the boxes both in the same state? Obviously these overlap: e.g. to be consistent, if you answered Y to 1. and N to 2., you'd also answer N to 3.
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So, for YNN, we learn that box 1 is definitely in state 0 and box 2 is definitely in state 1. We can represent this as the following probability distribution over possible pairs of states:pic.twitter.com/7XV6lwH2Cc
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OK, nothing very clever here! Now for an inconsistent set, NNN. Both boxes are in state 0, but... they're also in different states? Turns out you can still assign a 'probability' distribution. Sort of. Scare quotes because one 'probability' is negative:pic.twitter.com/P5v6tjbway
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Replying to @drossbucket
Did you mean “both in state 1,” or do I need coffee?
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Replying to @Meaningness
Ugh! It's me that needs the coffee. I knew I'd mess up somewhere with lots of fiddly sign stuff like this!
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I think expositionally would be cleaner if the signs were flipped so Y=1, N=0. (I kept being confused by this. But I’m a computer guy.)
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Replying to @Meaningness
Yeah, probably. There may have been some consistency reason for wanting it this way but I don't remember it now. I absolutely hate thinking about notation, it's the worst.
0 replies 0 retweets 1 likeThanks. Twitter will use this to make your timeline better. UndoUndo
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