Comment by p1necone
5 days ago
Worth noting that solution only works if the false positives are totally random, which is probably not true of many real world cases and would be pretty hard to work out.
5 days ago
Worth noting that solution only works if the false positives are totally random, which is probably not true of many real world cases and would be pretty hard to work out.
Definitely. Real world adds lots of complexities and nuances, but I was just trying to make the point that it matters how those inferences compound. That we can't just conclude that compounding inferences decreases likelihood
Well they were talking about a chain, A->B, B->C, C->D.
You're talking about multiple pieces of evidence for the same statement. Your tests don't depend on any of the previous tests also being right.
Be careful with your description there, are you sure it doesn't apply to the Bayesian example (which was... illustrative...? And not supposed to be every possible example?)? We calculated f(f(f(x))), so I wouldn't say that this "doesn't depend on the previous 'test'". Take your chain, we can represent it with h(g(f(x))) (or (f∘g∘h)(x)). That clearly fits your case for when f=g=h. Don't lose sight of the abstractions.
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