faint asteroids; statistical significance in dollar units

In a day shortened by health issues, I did get in a good conversation with David Schlegel (LBL), Aaron Meisner (LBL), and Dustin Lang on asteroid detection below the “plate limit”. That is, if we have multi-epoch imaging spread out over time, and we want to find asteroids, do we have to detect objects in each individual exposure or frame and then line up the detections into orbits, or can we search without individual-image detections? Of course the answer is we don't have to detect first, and we can find things below the individual-image detection limits. Meisner has even shown this to be true for the WISE data. We discussed how to efficiently search for faint, Earth-crossing (or impacting) asteroids.

I had lunch with luminary David Donoho (Stanford); we discussed a very clever of idea of his regarding significance thresholds (like five-sigma or ten-sigma): The idea is that a five-sigma threshold is only interesting if it is unlikely that the investigator would have come to this threshold by chance. As computers grow and data-science techniques evolve, it is easier to test more and more hypotheses, and therefore accidentally find (say) five-sigma results. Really the question should be: How expensive would it be to find this result by chance? That is, how much computation would I have to do on a “null” data set to accidentally discover a result of this significance? If the answer is “$5000 of Amazon EC2 time” then the result isn't really all that significant, even if it is many sigma! If the answer is “a billion dollars“ it is, probably, significant. We expanded on this idea in a number of directions, including what it would take to keep such calculations (translations of significance into dollars) up-to-date, and how to get this project funded!

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