Foreman-Mackey and I had a long conversation about parameterizing exoplanet models for transit lightcurves (and also radial-velocity measurements, direct-detection experiments, and astrometric data). The issue is that there are multiple angles—between the orbital plane and the plane normal to the line of sight, between the line of sight and the perihelion direction, and between the perihelion and both the ascending node and the fiducial time (zero of time). These angles are all differently degenerate for different kinds of data, and a well-measured angle can be
hidden if you parameterize it such that the well-measured angle appears as a difference or sum of parameters. We also pair-coded some improvements to his transit-fitting code. The fits—to Kepler and Spitzer data—are sweet. Because his code is flexible, he can learn the limb darkening along with all the orbit and transit parameters.
At applied-math-meets-astronomy group meeting, we discussed various things, including using classification within a sampler to split the parameter space (in which there is a multi-modal likelihood function or posterior PDF) into a set of unimodal sub-models. On this subject, it is great to have Muandet visiting from MPI-IS; he is an expert on support vector machines and their extensions. Another thing that we discussed is the possibility in the Goodman & Weare stretch move underlying emcee and Hou's code, we might be able to improve the acceptance rate by changing the proposal distribution in the one-dimensional walker-mixing direction. That is super cool and something to work on at sleep time.