bayess’ back! [on CRAN]

free Springer textbooks [incl. Bayesian essentials]

ENSEA & CISEA 2019

I found my (short) trip to Abdijan for the CISEA 2019 conference quite fantastic as it allowed me to meet with old friends, from the earliest days at CREST and even before, and to meet new ones. Including local students of ENSEA who had taken a Bayesian course out of my Bayesian Choice book. And who had questions about the nature of priors and the difficulty they had in accepting that several replies were possible with the same data! I wish I had had more time to discuss the relativity of Bayesian statements with them but this was a great and rare opportunity to find avid readers of my books! I also had a long chat with another student worried about the use or mis-use of reversible jump algorithms to draw inference  on time-series models in Bayesian Essentials, chat that actually demonstrated his perfect understanding of the matter. And it was fabulous to meet so many statisticians and econometricians from West Africa, most of them French-speaking. My only regret is not having any free time to visit Abidjan or the neighbourhood as the schedule of the conference did not allow for it [or even for a timely posting of a post!], especially as it regularly ran overtime. (But it did provide for a wide range of new local dishes that I definitely enjoyed tasting!) We are now discussing further opportunities to visit there, e.g. by teaching a short course at the Master or PhD levels.

mea culpa!

An entry about our Bayesian Essentials book on X validated alerted me to a typo in the derivation of the Gaussian posterior..! When deriving the posterior (which was left as an exercise in the Bayesian Core), I just forgot the term expressing the divergence between the prior mean and the sample mean. Mea culpa!!!

relabelling in Bayesian mixtures by pivotal units

Yet another paper on relabelling for mixtures, when one would think everything and more has already be said and written on the topic… This one appeared in Statistics and Computing last August and I only became aware of it through ResearchGate which sent me an unsolicited email that this paper quoted one of my own papers. As well as Bayesian Essentials.

The current paper by Egidi, Pappadà, Pauli and Torelli starts from the remark that the similarity matrix of the probabilities for pairs of observations to be in the same component is invariant to label switching. A property we also used in our 2000 JASA paper. But here the authors assume it is possible to find pivots, that is, as many observations as there are components such that any pair of them is never in the same component with posterior probability one. These pivots are then used for the relabelling, as they define a preferential relabelling at each iteration. Now, this is not always possible since there are presumably iterations with empty components and there is rarely a zero probability that enough pairs never meet. The resolution of this quandary is then to remove the iterations for which this happens, a subsampling that changes the nature of the MCMC chain and may jeopardise its Markovian validation. The authors however suggest using alternative and computationally cheaper solutions to identify the pivots. (Which confuses me as to which solution they adopt.)

The next part of the paper compares this approach with seven other solutions found in the literature, from Matthew Stephens’ (2000) to our permutation reordering. Which does pretty well in terms of MSE in the simulation study (see the massive Table 3) while being much cheaper to implement than the proposed pivotal relabelling (Table 4). And which, contrary to the authors’ objection, does not require the precise computation of the MAP since, as indicated in our paper, the relative maximum based on the MCMC iterations can be used as a proxy. I am thus less than convinced at the improvement brought by this alternative…