Today was my last day and fifth lecture at TASI. This lecture was crowd-sourced in content! I spoke about Fisher information, linear algebra tips and tricks, and decision theory and model selection. On the latter I strongly advocated engineering methods like cross-validation!
Over lunch I had a great set of conversations with Zach Berta-Thompson about precise measurement for exoplanets, and also hack weeks like the #GaiaSprint. We went deep into the limits on ultra-precise photometry from the ground. We wondered at the point that the best imaging systems get the best precision (on photometry, of point sources) by de-focusing. That has always struck me as somehow absurd, though it's true that you don't have to understand your system nearly so well when you are out of focus (for many reasons).
We had one very good idea: Instead of de-focusing, put in an objective prism! You could get many of the benefits of de-focus but also get far more information about the atmosphere and speckle and scintillation and so on. In principle, you might beat the best measurements made to date. And it is a cheap experiment to perform.