Archive for Valencia 3

a jump back in time

Posted in Books, Kids, Statistics, Travel, University life with tags , , , , , , , , , , , on October 1, 2018 by xi'an

As the Department of Statistics in Warwick is slowly emptying its shelves and offices for the big migration to the new building that is almost completed, books and documents are abandoned in the corridors and the work spaces. On this occasion, I thus happened to spot a vintage edition of the Valencia 3 proceedings. I had missed this meeting and hence the volume for, during the last year of my PhD, I was drafted in the French Navy and as a result prohibited to travel abroad. (Although on reflection I could have safely done it with no one in the military the wiser!) Reading through the papers thirty years later is a weird experience, as I do not remember most of the papers, the exception being the mixture modelling paper by José Bernardo and Javier Giròn which I studied a few years later when writing the mixture estimation and simulation paper with Jean Diebolt. And then again in our much more recent non-informative paper with Clara Grazian.  And Prem Goel’s survey of Bayesian software. That is, 1987 state of the art software. Covering an amazing eighteen list. Including versions by Zellner, Tierney, Schervish, Smith [but no MCMC], Jaynes, Goldstein, Geweke, van Dijk, Bauwens, which apparently did not survive the ages till now. Most were in Fortran but S was also mentioned. And another version of Tierney, Kass and Kadane on Laplace approximations. And the reference paper of Dennis Lindley [who was already retired from UCL at that time!] on the Hardy-Weinberg equilibrium. And another paper by Don Rubin on using SIR (Rubin, 1983) for simulating from posterior distributions with missing data. Ten years before the particle filter paper, and apparently missing the possibility of weights with infinite variance.

There already were some illustrations of Bayesian analysis in action, including one by Jay Kadane reproduced in his book. And several papers by Jim Berger, Tony O’Hagan, Luis Pericchi and others on imprecise Bayesian modelling, which was in tune with the era, the imprecise probability book by Peter Walley about to appear. And a paper by Shaw on numerical integration that mentioned quasi-random methods. Applied to a 12 component Normal mixture.Overall, a much less theoretical content than I would have expected. And nothing about shrinkage estimators, although a fraction of the speakers had worked on this topic most recently.

At a less fundamental level, this was a time when LaTeX was becoming a standard, as shown by a few papers in the volume (and as I was to find when visiting Purdue the year after), even though most were still typed on a typewriter, including a manuscript addition by Dennis Lindley. And Warwick appeared as a Bayesian hotpot!, with at least five papers written by people there permanently or on a long term visit. (In case a local is interested in it, I have kept the volume, to be found in my new office!)

Another history of MCMC

Posted in Books, Statistics, University life with tags , , , , , on April 20, 2011 by xi'an

In the most recent issue of Statistical Science, the special topic is “Celebrating the EM Algorithm’s Quandunciacentennial“. It contains an historical survey by Martin Tanner and Wing Wong on the emergence of MCMC Bayesian computation in the 1980’s, This survey is more focused and more informative than our global history (also to appear in Statistical Science). In particular, it provides the authors’ analysis as to why MCMC was delayed by ten years or so (or even more when considering that a Gibbs sampler as a simulation tool appears in both Hastings’ (1970) and Besag‘s (1974) papers). They dismiss [our] concerns about computing power (I was running Monte Carlo simulations on my Apple IIe by 1986 and a single mean square error curve evaluation for a James-Stein type estimator would then take close to a weekend!) and Markov innumeracy, rather attributing the reluctance to a lack of confidence into the method. This perspective remains debatable as, apart from Tony O’Hagan who was then fighting again Monte Carlo methods as being un-Bayesian (1987, JRSS D),  I do not remember any negative attitude at the time about simulation and the immediate spread of the MCMC methods from Alan Gelfand’s and Adrian Smith’s presentations of their 1990 paper shows on the opposite that the Bayesian community was ready for the move.

Another interesting point made in this historical survey is that Metropolis’ and other Markov chain methods were first presented outside simulation sections of books like Hammersley and Handscomb (1964), Rubinstein (1981) and Ripley (1987), perpetuating the impression that such methods were mostly optimisation or niche specific methods. This is also why Besag’s earlier works (not mentioned in this survey) did not get wider recognition, until later. Something I was not aware is the appearance of iterative adaptive importance sampling (i.e. population Monte Carlo) in the Bayesian literature of the 1980’s, with proposals from Herman van Dijk, Adrian Smith, and others. The appendix about Smith et al. (1985), the 1987 special issue of JRSS D, and the computation contents of Valencia 3 (that I sadly missed for being in the Army!) is also quite informative about the perception of computational Bayesian statistics at this time.

A missing connection in this survey is Gilles Celeux and Jean Diebolt’s stochastic EM (or SEM). As early as 1981, with Michel Broniatowski, they proposed a simulated version of EM  for mixtures where the latent variable z was simulated from its conditional distribution rather than replaced with its expectation. So this was the first half of the Gibbs sampler for mixtures we completed with Jean Diebolt about ten years later. (Also found in Gelman and King, 1990.) These authors did not get much recognition from the community, though, as they focused almost exclusively on mixtures, used simulation to produce a randomness that would escape the local mode attraction, rather than targeting the posterior distribution, and did not analyse the Markovian nature of their algorithm until later with the simulated annealing EM algorithm.