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Good_Burning_Plastic comments on Geometric Bayesian Update - Less Wrong
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Comments (9)
There's no reason why P(E|H) and P(E|~H) must sum to 1, but I can't move the lower right corner without the whole diagram rescaling.
Of course you are right, but it would just be a linear transformation of the whole diagram, so it doesn't change anything in the result. I've built the diagram starting from a square, so I can't change this easily... just imagine the whole thing scaling on the X axis, OK?
Edit: since two people asked for this, I remade the diagram and now you can put in any values of P(E|H) and P(E|~H)
When I drag the dot for P(E|~H), it only changes P(E|~H), but when I drag the dot for P(E|H), it still keeps P(E|H)+P(E|~H) conserved, which is a little weird. I think it would be better if changing either of them did not affect the other.
Agreed. The diagram strongly suggests that they do sum to one, so this geometrical method is more confusing than helpful.