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Comment by tunesmith | Hacker News Reader

"More than 90 percent of those (extinction-level) asteroids, which are 1 kilometer, 0.62 miles, or larger, have already been identified by NASA and its partners."

How do they know it's 90%? I mean, if the denominator is unknown? If the denominator is known, then doesn't that mean they've identified them?

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Abundance estimation is a big problem in ecology (and other fields), and they’ve developed some clever ways to estimate population sizes without doing an exhaustive census.

One popular approach is a capture-recapture experiment. On your first trip, you find as many of your targets as possible and mark each one. With turtles, you might paint something on the shell; here, it might be something like determining its orbit and other characteristics. You wait a bit, and search again (starting from scratch), but this time you separately record the number of “new” specimens and the number recaptured. A tiny bit of algebra from these three numbers gives you an estimate of the population size.

It comes with a bias though, since your searches will bias towards finding asteroids that are easiest to find using your search method.

Show me a measurement that doesn't come with bias

I have one apple.

Oops, it was an Asian pear: https://en.wikipedia.org/wiki/Pyrus_pyrifolia

You took a bite off it though, so your measurement is in fact biased. Other people might measure 0.75 apple instead.

Survivorship bias

Correct, and since that bias is towards larger NEOs, which are relatively easier to detect then smaller objects, they can be reasonably confident about that estimate. It is the medium to small size NEOs that are the most worrisome. They are harder to detect, and hence harder to estimate how many are out there.

Seems like a bigger problem for turtles than for asteroids.

I mean, asteroids don't deliberately hide.

Sure, some are darker and/or have a less visible radar profile or whatever, but the variations seem manageable.

They don't deliberately hide, but (as mentioned in the article) they can vary dramatically in how visible they are to us over time if, for example, they have a highly eccentric orbit.

It’s a statistical argument based on the observed distribution of asteroids. It’s not precisely true, and could even be widely incorrect, but they think it’s likely to be in the correct neighborhood.

Also, after a certain size things become significantly easier to detect with your existing instruments, so there is some confidence from that.

Related to this (though maybe not directly applicable), in certain scenarios there is a difference between what can be reliably detected vs tracked. For example, in the context of debris orbiting the earth, our radars can take LEO census measurements down to 3-4mm, even though we can only reliably track things on the ~10cm size range.

We can therefore semi-confidently say we know how many 1cm objects there are out there, even if we can’t predict the trajectory of any single one. (Similar to atoms, really)

The mark-recapture method has been mentioned. Additionally, you can create fake data and run it through your search algorithm to get an estimate of your detection efficiency.

IIRC, the 90% estimate is based on how often searches encounter previously cataloged objects.

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