A revised assessment of nested sampling

As announced earlier on that post, the MaxEnt2009 meeting was a very good opportunity to revise a second time our nested sampling evaluation, written with Nicolas Chopin. The new version is now posted on arXiv as well as resubmitted to Biometrika. The changes in the text are presumably less important than those in our (my?) understanding of the method. I indeed think the nested sampling method belongs to the general category of importance sampling methods and that potential improvements lie in modifying the evaluation of the prior mass between slices of the likelihood.I still have to understand better why nested sampling would be the only importance solution in a given problem, as argued for instance in this recent posting on arXiv by Livi Pártay, Albert Bartók, and Gábor Csányi, from Cambrdige University, which was presented earlier this week at the MaxEnt2009 meeting, but this will have to wait till the Fall, I am afraid…