If you’ve discovered this new page (new, as of 5 September 2015) then welcome to what I hope will become an open, collaborative project with two aims:
(1) to provide a convergence proof for ‘real’ nested sampling: that is, nested sampling in which sampling of the likelihood-constrained posterior is performed via MCMC (as in the classic ‘lighthouse’ example); and
(2) come up with practical applications that (i) break nested sampling without breaking SMC, and (ii) break SMC without breaking nested sampling.
Obviously both aims require some clarification if we’re to begin making progress; and indeed that will be an evolving part of the project. For now I will place a precis (as opposed to precise!) description of what I think are sensible starting points for each under the two subpages of this tab (click on “Nested Sampling” to see dropdown menu), and I will edit these to keep them updated as appropriate.
Q. Why blog this?
A. Because I can never have too much attention, me me me. 🙂 No, in fact, I’m blogging this because (i) writing about it publicly is supposed to keep me motivated; (ii) it’s hard to have an open collaboration without an open front page; and (iii) because I think it might be genuinely interesting even for people not participating actively in the project to follow some of the topics (e.g. MCMC theory, different types of stochastic convergence) that will inevitably be covered.
Q. Who can participate?
A. Anyone (with at least a minimal understanding of nested sampling, SMC and/or statistics generally). At first I hope that interested parties will be revealed through the comments box, and eventually I envisage the most active contributors being given access to edit the page directly.
Q. Why participate?
A. Because you’re interested in the project. Because you long for the reassurances that a convergence proof would give to nested sampling with MCMC. Because you think nested sampling is a load of bollocks in comparison to SMC and you’ve got a bunch of examples where it doesn’t work as well. Because you think the proof is trivial and that I’m stupid for even asking. Some other reason.
Q. Am I going to steal your ideas?
A. No, if this project amounts to something publishable I would of course invite any relevant contributors to collaborate on a paper; and likewise I will not take any ideas as my own for that purpose or any other. I also suspect that some ‘old-fashioned’ journals would not accept something that was previously published online, in any case.
Q. Am I worried that you’ll steal my ideas?
A. Not really, it’s not exactly a Millennium Prize problem. Even if you come along, get some ideas and then figure out a way to complete the proof and go publish it yourself I’ll be a bit upset, but if it leads to something useful to me (i.e. a convergence proof with some intuition as to how long to run the MCMC steps, what type of problems are readily amenable to nested sampling, etc.) then I’ll get over it.
Q. Does that mean you cede copyright to all this?
A. No. Quite the opposite.