Today was the fourth day of #AstroHackWeek 2016. My goodness is everyone tired! A week of 10-to-15-hour days is a bit too much! Fortunately, the crowd was woken up by two awesome talks on optimization, one by Yu Feng (UCB) and one by Grigor Aslanyan (UCB). Feng talked about optimization in general, classifying methods, and helping us to understand the use of gradients and hessians, and trust regions. Aslanyan focused on the use of optimization to solve linear-algebra problems, and explained extremely clearly the conjugate gradient method. These talks, taken together, constituted the best live introduction to optimization I have ever seen. These were followed by Dan Foreman-Mackey (UW), who explained, in his usual extremely clear and engaging way, the basics of sampling, assessing convergence, and presentation of sampling-based results. So excited to get our pedagogical paper on MCMC out there.
I pair-coded with Adrian Price-Whelan (Princeton) our new project to sample the single-line binary star (or expolanet) system exactly using Simple Monte Carlo. Our innovation is to sample explicitly only in the non-linear parameters, and to deal with the linear parameters through exact marginalization at the rejection step, and through exact sampling at the output step. This all seems to work, and we can see the posterior pdf become less multi-moded as the number (or density) of observations increases.
Meanwhile, Dalya Baron (TAU) and Matt Mechtley (ASU) changed the toy microscopy problem to a better test problem (we had too much symmetry in our toy “molecule”). Everything works end-to-end, so in the end-of-day stand-up meeting, Baron stood up and explained our marginalized likelihood and how we are optimizing it, and Mecthley showed the data and the results. These pretty-much shocked the audience: Our images are so bad (a few photons each) and yet such a complex molecule can be inferred. We ended the day by discussing what directions to go next with this; I am a bit confused about the scope for paper one.