finding good priors

In a secret "overwhelming force" project, Foreman-Mackey is resampling all the Kepler Objects of Interest, to produce a full probabilistic catalog. In many low signal-to-noise systems, there are fitting degeneracies (really near-degeneracies). In many of these, the posterior pdf does not accord with our intuitive views about what ought to be going on. We realized that this is because our "flat priors" didn't accord with our real, prior beliefs. That is, there was a disparity between our actual prior beliefs and our coded-up prior function. We knew this would be the case—we are using wrong but simple interim priors that we plan to replace with a hierarchical inference—but it was amusing to be reminded of the the simple point that ugly priors lead to ugly inferences. We made some small changes to the priors, resampled, and our inferences look much better.

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