I have published one paper and have two more in the works under the subject measuring the undetectable. My evil plan is panning out; today Joey Richards, James Long (Berkeley), Dan Foreman-Mackey, and I all agreed that we should work together on a very nice and extremely practical project. Here it is:
Imagine you have a catalog of point-source fluxes, measured for a bunch of sources in a badly documented multi-epoch survey. Now imagine that you are looking at one source, which is variable, and it has been detected at some epochs and not at others. Imagine further that at the non-detect epochs, you are not provided with any information about the flux upper limits; all you know is that the source wasn't seen
. How do you fit the stellar (lightcurve) properties of this source, using both the detections and the non-detections?
Without priors, this is impossible, I think, because you don't know whether the non-detections are non-detections because the data at those epochs was extremely bad or whether they are non-detections because the star at those epochs was very faint. But we figured out what you could do if you could hierarchically infer a prior over the detection threshold and over the noise properties of the detected sources. We started to write documents and code in the afternoon.
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