More generally, if you want a good estimate of the near-term probability of impact events, you probably want to survey one or several of the other bodies in the solar system. They have an impact record relatively untainted by anthropic bias, and also have the advantage of being a lot easier to read, lacking the plate tectonics that tend to wipe out a lot of older geology on Earth.
And this has been done. We have good records of impact levels on the Moon, Mars and Jupiter (although Jupiter is a little weird). It doesn't look like there's heavy anthropic bias there.
We have good records of impact levels on the Moon, Mars and Jupiter (although Jupiter is a little weird).
Ćirković, Sandberg & Bostrom refer to these briefly in the paper, but seem to think they're not adequate or as relevant:
...For instance, the asteroidal and cometary impact history of the solar system is, in theory, easier to obtain for the Moon, where the erosion is orders of magnitude weaker than on Earth. In practice, this is still not feasible for obtaining the fair sampling of the impactors because: (1) precise dating of a large set of lunar c
From a paper by Milan M. Ćirković, Anders Sandberg, and Nick Bostrom:
There cannot have been a large disaster on Earth in the last millennia, or we wouldn't be around to see it. There can't have been a very large disaster on Earth in the last ten thousand years, or we wouldn't be around to see it. There can't have been a huge disaster on Earth in the last million years, or we wouldn't be around to see it. There can't have been a planet-destroying disaster on Earth... ever.
Thus the fact that we exist precludes us seeing certain types of disasters in the historical record; as we get closer and closer to the present day, the magnitude of the disasters we can see goes down. These missing disasters form the "anthropic shadow", somewhat visible in the top right of this diagram:
Hence even though it looks like the risk is going down (the magnitude is diminishing as we approach the present), we can't rely on this being true: it could be a purely anthropic effect.