I spent most of #astrohackny arguing with Jeff Andrews (Columbia) about white-dwarf cooling age differences and how to do inference given measurements of white dwarf masses and cooling times (for white dwarfs in coeval binaries). The problem is non-trivial and is giving Andrews biased results. In the end we decided to obey the advice I usually give, which is to beat up the likelihood function before doing the full inference. Meaning: Try to figure out if the inference issues are in the likelihood function, the prior, or the MCMC sampler. Since all these things combine in a full inference, it makes sense to "unit test" (as it were) the likelihood function first.
Late in the day I discussed the CMB likelihood function with Evan Biederstedt. Our goal is to show that we can perform a non-approximate likelihood function evaluation in real space for a non-uniformly observed CMB sky (heteroskedastic and cut sky). This involves solving—and taking the determinant of—a large matrix (50 million squared in the case of Planck). I, for one, think we can do this, using our brand-new linear algebra foo.