This is done by matching up the predictions made by Einstein's Field Equations about this kind of event to the actual observations.
Does this not bring in a natural bias towards confirming what you expect to confirm? How can we be sure that what was measured was the result of gravitational waves from 100 billion light years away or whatever, and not as a result of something else, such as a small earthquake in China, or something ridiculous like that?

It seems to me that we're confirming gravitational waves based on some heavy assumptions. We seem to be "proving" Einstein's equations simply by applying them.

I'm not for a minute suggesting they're wrong, by the way. I'm just don't understand how they can use theoretical equations to confirm the theory which those equations are based on. Something doesn't add up, and I can't quite put my finger on it.