Back home in Oxford/Witney after a brutally tiring week of meetings in Seattle; feeling nevertheless reinvigorated to crack on with some hardcore stats and in doing so hopefully contribute (in some tiny bee’s dick of a way; as they say in the building trade) to the eventual elimination of malaria within our lifetime!
Scanning astro-ph for some blog fodder I decided to read up on the latest paper by Porter & Cornish entitled “Fisher vs. Bayes: A comparison of parameter estimation techniques for massive black hole binaries to high redshifts with eLISA“. It’s a long-ish manuscript which recalled for me a particular monologue from The Pale King, in which one of the tax inspectors is working his way to a grand point about the American life but can’t quite find the words to do anything other than circle endlessly around it. In brief, the problem addressed by this paper concerns a disagreement between the confidence intervals on the parameters of hypothetical GW observations suggested by a Fisher information approach and the credible intervals suggested by a Bayesian approach. While the authors’ discussion hints at a number of possible origins for the difference—the unusual topology of the model’s parameter space; the frequent presence of bimodality in the likelihood surface; ill-conditioning of the information matrix—one yet feels by the paper’s end that they have not quite been able to identify any central truth. I suspect this is because the authors’ have not gone sufficiently far in their own investigation of classical statistics to clarify the issue. For instance, there is no distinction made in the paper between the Fisher information matrix and the observed information matrix (cf. Efron & Hinkley); nor any direct attempt to test the regularity conditions on the Cramer-Rao bound that would lead us to expect nice behaviour in the MLE in the first place.
Finally, an observation not entirely tangential to the above is to note that despite the assertion, “This type of MCMC algorithm is commonly referred to as Hessian MCMC …”, a google search yields no true positive results other than links to the first author’s own papers (and perhaps eventually this blog post).