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pnrjulius comments on Absence of Evidence Is Evidence of Absence - Less Wrong
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This is all fine and good, but it does not address what "evidence" is. I cannot gather evidence of extra solar planets (either evidence for or against existence) with my naked eyes. So in this experiment, even though I see no "evidence" of extra solar planets by looking up into the sky, I still do not have evidence of absense, because in fact I have no evidence at all.
Evidence, from the aspect of probability theory, is only meaningful when the experiment is able to differential between existence and absence.
Then the real question becomes: do we have evidence that our experiment is able to yield evidence? And the only way to prove this to the affirmative, is to find something. You cannot *know* you experiment is designed correctly.
There is another way: Look really really hard with tools that would be expected to work. If you find something? Yay, your hypothesis is confirmed. If you don't? You'd better start doubting your hypothesis.
You already do this in many situations I'm sure. If someone said, "You have a million dollars!" and you looked in your pockets, your bank accounts, your stock accounts (if any), etc. and didn't find a million dollars in them (or collectively in all of them put together), you would be pretty well convinced that the million dollars you allegedly have doesn't exist. (In fact, depending on your current economic status you might have a very low prior in the first place; I know I would.)