Science

When does successful prediction provide strong evidence?

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Here's a sort of rule-of-thumb answer that I find useful. Roughly, we should ask ourselves how surprising the evidence would be if the hypothesis were not true. Suppose the question is whether Harvey robbed the bank. Our evidence for Harvey being the thief is that a witness saw him outside the bank around the time of the robbery. If Harvey really is the robber, this isn't unlikely, but suppose Harvey works in the barber shop on the block where the bank is, and the time he was seen was a few minutes before opening time for the barber shop. Then seeing him outside the bank wouldn't be surprising even if he wasn't the robber. It's not strong evidence.

On the other hand, suppose the evidence is that a search of Harvey's apartment turns up a large bag of bills whose serial numbers identify them as the ones that were stolen.Then things look bad for Harvey. If he wasn't the robber, it would be surprising to find the money in his apartment. (Of course, this isn't conclusive proof. Maybe someone has planted the money to frame Harvey.)

That's the rough version. What really matters is the ratio of two probabilities: the probability of the evidence assuming the hypothesis is true (write that as p(E|H), and the probability of the evidence assuming the hypothesis is false (write that as p(E|not-H). The ratio

p(E|H)
p(E|not-H)

is called the likelihood ratio. The higher the likelihood ratio, the stronger the evidence.

There's a good deal more to be said, but the little test sketched here is especially useful in its negative form. If the evidence isn't surprising by this test, then it's not strong.

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