Fisher matrix manipulations

Not much happened today, research-wise. But one great thing was a short call with Ana Bonaca, in which we reviewed what we are doing with our Fisher matrices. We are doing the right things! There are two operations you want to do: Change variables, and marginalize out nuisances. These look pretty different. That is, if you just naively change variables to a single variable, and don't marginalize out anything, the operation is an outer product, with the Fisher matrix as metric, but it is equivalent to assuming that all else is fixed. That is, it slices your likelihood. This is not usually the conservative move, which is to either marginalize (if you are Bayesian) or profile (if you are frequentist). These operations involve inverses of Fisher matrices. Some of the relevant details are in section 2 of this useful paper.