causal pixel modeling, day 4

Foreman-Mackey re-started exoplanet search (in Kepler) last night, and on the train home from Tübingen we looked at some of the early false positives. We realized that the way we are constructing the search leads to some non-trivial issues: For performance reasons, we slide a single "box" model across the lightcurve once, and then we do search by linking together likelihood increments from the one-d box slide in periodic groups. The issue is: When we slide the box, we permit the box to take any transit depth, so the system can link together in a periodic group a set of transit-like excursions that all have different depths. A true exoplanet transit signal has a (nearly) fixed depth.

The solution (and this brings back memories of GALEX) is to combine the periodic box results both with and without a constraint that the depths must be identical. The identical model must beat the non-identical model for something to make the search cut. The one complexity is that we have to penalize model complexity: The likelihood of the non-uniform depths model is always better at maximum, because it has much more freedom.

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