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Thomas comments on What was your biggest recent surprise? - Less Wrong Discussion
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The same way we could obtain details from an astronomy video. One hour of a video of a distant planet might be worth of a big telescope, The long exposition time was the first step in this direction, long ago.
The current exo planet detection is another, bigger.
We simply don't yet use every information we have.
Astronomy is an interesting connection to think about wrt to this work. In astronomy, we're integrating the light received. In some sense this is dynamic, because there are small variations due to atmosphere. But the underlying signal is assumed to be static? I guess there are pulsars where we don't expect that. Maybe then people have to apply similar techniques (filtering out dynamics, e.g. from atmosphere, at frequencies far from that expected from pulsars?)
You, an astronomer, should always ask yourself: Giving this light pattern in time, what is the most probable source which would give me this pattern. Be it static or dynamic, whichever fits the best.
The standard approach is to simulate multiple possible sources and use Bayesian techniques, such as maximum likelihood, to evaluate which ones match the data best and whether the best is a good enough fit. The waveforms matching in LIGO is one of the extremes, given how weak the potential signal is.