an introduction to MCMC sampling

Following a rather clueless question on X validated, I had a quick read of A simple introduction to Markov Chain Monte–Carlo sampling, by Ravenzwaaij, Cassey, and Brown, published in 2018 in Psychonomic Bulletin & Review, which I had never opened to this day. The setting is very basic and the authors at pain to make their explanations as simple as possible, but I find the effort somehow backfires under the excess of details. And the characteristic avoidance of mathematical symbols and formulae. For instance, in the Normal mean example that is used as introductory illustration and that confused the question originator, there is no explanation for the posterior being a N(100,15) distribution, 100 being the sample average, the notation N(μ|x,σ) is used for the posterior density, and then the Metropolis comparison brings an added layer of confusion:

“Since the target distribution is normal with mean 100 (the value of the single observation) and standard deviation 15,  this means comparing N(100|108, 15) against N(100|110, 15).”

as it most unfortunately exchanges the positions of  μ and x (which is equal to 100). There is no fundamental error there, due to the symmetry of the Normal density, but this switch from posterior to likelihood certainly contributes to the confusion of the QO. Similarly for the Metropolis step description:

“If the new proposal has a lower posterior value than the most recent sample, then randomly choose to accept or
reject the new proposal, with a probability equal to the height of both posterior values. “

And the shortcomings of MCMC may prove equally difficult to ingest: like

“The method will “work” (i.e., the sampling distribution will truly be the target distribution) as long as certain conditions are met.
Firstly, the likelihood values calculated (…) to accept or reject the new proposal must accurately reflect the density of the proposal in the target distribution. When MCMC is applied to Bayesian inference, this means that the values calculated must be posterior likelihoods, or at least be proportional to the posterior likelihood (i.e., the ratio of the likelihoods calculated relative to one another must be correct).”

which leaves me uncertain as to what the authors do mean by the alternative situation, i.e., by the proposed value not reflecting the proposal density. Again, the reluctance in using (more) formulae hurts the intended pedagogical explanations.

computing Bayes 2.0

Our survey paper on “computing Bayes“, written with my friends Gael Martin [who led this project most efficiently!] and David Frazier, has now been revised and resubmitted, the new version being now available on arXiv. Recognising that the entire range of the literature cannot be encompassed within a single review, esp. wrt the theoretical advances made on MCMC, the revised version is more focussed on the approximative solutions (when considering MCMC as “exact”!). As put by one of the referees [which were all very supportive of the paper], “the authors are very brave. To cover in a review paper the computational methods for Bayesian inference is indeed a monumental task and in a way an hopeless one”. This is the opportunity to congratulate Gael on her election to the Academy of Social Sciences of Australia last month. (Along with her colleague from Monash, Rob Hyndman.)

Rao-Blackwellisation, a review in the making

Recently, I have been contacted by a mainstream statistics journal to write a review of Rao-Blackwellisation techniques in computational statistics, in connection with an issue celebrating C.R. Rao’s 100th birthday. As many many techniques can be interpreted as weak forms of Rao-Blackwellisation, as e.g. all auxiliary variable approaches, I am clearly facing an abundance of riches and would thus welcome suggestions from Og’s readers on the major advances in Monte Carlo methods that can be connected with the Rao-Blackwell-Kolmogorov theorem. (On the personal and anecdotal side, I only met C.R. Rao once, in 1988, when he came for a seminar at Purdue University where I was spending the year.)

open reviews

When looking at a question on X validated, on the expected Metropolis-Hastings ratio being one (not all the time!), I was somewhat bemused at the OP linking to an anonymised paper under review for ICLR, as I thought this was breaching standard confidentiality rules for reviews. Digging a wee bit deeper, I realised this was a paper from the previous ICLR conference, already published both on arXiv and in the 2018 conference proceedings, and that ICLR was actually resorting to an open review policy where both papers and reviews were available and even better where anyone could comment on the paper while it was under review. And after. Which I think is a great idea, the worst possible situation being a poor paper remaining un-discussed. While I am not a big fan of the brutalist approach of many machine-learning conferences, where the restrictive format of both submissions and reviews is essentially preventing in-depth reviews, this feature should be added to statistics journal webpages (until PCIs become the norm).

ABC intro for Astrophysics

Today I received in the mail a copy of the short book published by edp sciences after the courses we gave last year at the astrophysics summer school, in Autrans. Which contains a quick introduction to ABC extracted from my notes (which I still hope to turn into a book!). As well as a longer coverage of Bayesian foundations and computations by David Stenning and David van Dyk.