## Gibbs for kidds

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , , on February 12, 2018 by xi'an

A chance (?) question on X validated brought me to re-read Gibbs for Kids, 25 years after it was written (by my close friends George and Ed). The originator of the question had difficulties with the implementation, apparently missing the cyclic pattern of the sampler, as in equations (2.3) and (2.4), and with the convergence, which is only processed for a finite support in the American Statistician paper. The paper [which did not appear in American Statistician under this title!, but inspired an animal bredeer, Dan Gianola, to write a “Gibbs for pigs” presentation in 1993 at the 44th Annual Meeting of the European Association for Animal Production, Aarhus, Denmark!!!] most appropriately only contains toy examples since those can be processed and compared to know stationary measures. This is for instance the case for the auto-exponential model

$f(x,y) \propto exp(-xy)$

which is only defined as a probability density for a compact support. (The paper does not identify the model as a special case of auto-exponential model, which apparently made the originator of the model, Julian Besag in 1974, unhappy, as George and I found out when visiting Bath, where Julian was spending the final year of his life, many years later.) I use the limiting case all the time in class to point out that a Gibbs sampler can be devised and operate without a stationary probability distribution. However, being picky!, I would like to point out that, contrary, to a comment made in the paper, the Gibbs sampler does not “fail” but on the contrary still “converges” in this case, in the sense that a conditional ergodic theorem applies, i.e., the ratio of the frequencies of visits to two sets A and B with finite measure do converge to the ratio of these measures. For instance, running the Gibbs sampler 10⁶ steps and ckecking for the relative frequencies of x’s in (1,2) and (1,3) gives 0.685, versus log(2)/log(3)=0.63, since 1/x is the stationary measure. One important and influential feature of the paper is to stress that proper conditionals do not imply proper joints. George would work much further on that topic, in particular with his PhD student at the time, my friend Jim Hobert.

With regard to the convergence issue, Gibbs for Kids points out to Schervish and Carlin (1990), which came quite early when considering Gelfand and Smith published their initial paper the very same year, but which also adopts a functional approach to convergence, along the paper’s fixed point perspective, somehow complicating the matter. Later papers by Tierney (1994), Besag (1995), and Mengersen and Tweedie (1996) considerably simplified the answer, which is that irreducibility is a necessary and sufficient condition for convergence. (Incidentally, the reference list includes a technical report of mine’s on latent variable model MCMC implementation that never got published.)

## two positions at opposite ends of the map [openings]

Posted in Statistics with tags , , , , , , , , on September 22, 2017 by xi'an

In the past days, I received emails about two openings in statistics, in the beautiful and attractive [if geographically opposed!] cities of Bath, Britain, and Vancouver, British Columbia, and in two great departments:

• The Department of Mathematical Sciences, University of Bath, UK is inviting applications for the posts of Professor of Statistics and Lecturer/Senior Lecture/Reader in Statistics. Deadline for application is Monday 16 October 2017.
• The Department of Statistics at the University of British Columbia (UBC) invites applications from outstanding new investigators for a tenure-track position at the rank of Assistant Professor. Computational Statistics is targeted as a priority area for the search. Deadline for application is November 1, 2017.

## 3rd conference on geometric science[s] of information

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on January 31, 2017 by xi'an

A call for contribution to the 3rd Conference on Geometric Science of Information that I was asked to advertise. (I would have used Sciences instead of Science.) With a nice background picture related to Adelard de Bath, who among other things in natural philosophy introduced the Hindu-Arabic numerals in Europe [and later to America, even though the use of Arabic numerals there may soon come to an end]. And which Latin translation of Euclid’s Elements includes the above picture. The conference is on November 7-9, 2017, in the centre of Paris (Écoles de Mines, next to Luxembourg). (As I cannot spot the registration rates of that conference on the website, I cannot at this stage bring full support to the conference!)

## position in Bath

Posted in Statistics, University life with tags , , , , , , on April 14, 2016 by xi'an

Dan Simpson pointed out to me the still open call for an assistant/associate professor (lecturer/reader) position in mathematical statistics at the University of Bath, Southwest England (Somerset to be exact), with a closing date of April 22, i.e., next week. Beside being located in a lovely town on a beautiful campus, this is certainly “a pretty great place to be an early career researcher” to quote from Dan, with an attractive PhD program. Check this link for details. [And you may notice I wisely abstained from cracking any joke about position in bath…]

## Julian Besag 1945-2010

Posted in Books, R, Statistics, University life with tags , , , , , on August 7, 2010 by xi'an

I have just learned that Julian Besag passed away last morning in Bristol after being admitted to the hospital two weeks ago. He was a leading figure of our field, a fiercely independent thinker, a brilliant statistician, and undoubtedly the clearest pretendent to having fathered MCMC. His influence on the field of spatial statistics will be felt for years, but he will be sorely missed… My first meeting with Julian was in 1993 in Laramie, Wyoming, and my last memory of him will be this visit George Casella and I made to Bath and Bristol in October 2008, and where Julian attended both of our talks as well as the dinner in Bath and the after-seminar beer in Bristol… He will be missed.