Talks at the Kepler meeting today continued, with the end of the day being the start of developing working groups to tackle scientific problems in collaboration.
Talk highlights included Berger (Duke) going through some very simple arguments about how Bayesian inference protects you from many statistical and model-selection pitfalls. He showed a real example where Bayesian inference gets a different answer from frequentist inference, in a scientific problem on which he had actually worked; it is related to the Jeffreys-Lindley paradox, which is about distinguishing models with zero effect from models with some (unknown) non-zero effect. Clyde (Duke) and Cisewski (CMU) talked (in different contexts) about importance sampling (rather than MCMC). Adaptive importance sampling is obviously a very powerful technique we ought to be thinking about. At lunch, Berger backed this up, strongly endorsing importance sampling with adaptive proposal distributions in contexts where you want the Bayesian Evidence. (Didn't I say yesterday that you never want that?) Cisewski also talked about Approximate Bayesian Computation, which she described as "a method of last resort". But it looks like it might be valuable for many astrophysics problems: It replaces the likelihood with a thresholded "distance" between statistics of the data and generated data samples. In some cases, it asymptotically approaches true inference. Her seminar also effectively answered a question posed yesterday by Ragozzine (Florida) about how to combine inferences based on statistics computed on the data! ABC FTW?
Another highlight was Christiansen (Ames) showing that she can insert transits into the pixel-level data, run the pipelines, and recover them. She is doing this to test completeness and selection and noise models. But it is just as interesting from an inference perspective; the fact that she can insert realistic transits means (in principle) that we could be fitting in the pixel domain. I would be pleased to be doing that. Also, she showed evidence that de-trending (fitting out instrumental and stellar variability effects) perhaps ought to be done in the pixel space, not the integrated lightcurve space?
In the afternoon, we crowd-sourced projects for further study and split-ish into working groups. Despite the fact that I am dying to infer the population parameters of long-period planets from data coming only from single (isolated) transits, I decided to join the de-trending and noise model group. We want to improve Kepler's sensitivity by understanding better the device trends and noise.