Mike Cushing (Toledo) and I discussed some pet peeves (of his, and mine) about data analysis and statistics in astrophysics. We both agreed that things would be much better if the standard data analysis or modeling paper started out by saying what the Right Thing To Do (tm) is (it pretty-much always involves probabilistic modeling), and then how what is actually being done is an approximation to the RTTD(tm). That would keep us clamped to justifiable methods, guide approximation, but not put undue methodological burden on already burdened, pragmatic astrophysicists. We also talked about a few specific data-analysis challenges.
Michelle Deady and Lawrence Anderson-Huang (both Toledo) and I discussed the inversion of (or solution of equations involving) very large matrices that are sparse. I pointed them to ARPACK, which is what scipy.sparse wraps. Sparse matrix methods have made a huge impact on my group; along with MCMC methods, they are among the most valuable potential contributions to astrophysics from applied math, but they are not yet well known. If you have a huge-ass matrix and it is sparse (many elements are zero or near zero in the relevant senses), then probably you aren't inverting it efficiently if you aren't using sparse methods!