From a paper by Milan M. Ćirković, Anders Sandberg, and Nick Bostrom:
We describe a signiﬁcant practical consequence of taking anthropic biases into account in deriving predictions for rare stochastic catastrophic events. The risks associated with catastrophes such as asteroidal/cometary impacts, supervolcanic episodes, and explosions of supernovae/gamma-ray bursts are based on their observed frequencies. As a result, the frequencies of catastrophes that destroy or are otherwise incompatible with the existence of observers are systematically underestimated. We describe the consequences of this anthropic bias for estimation of catastrophic risks, and suggest some directions for future work.
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.