**I** came over the weekend across this graph and the associated news that the county of Saint-Nazaire, on the southern border of Brittany, had a significantly higher rate of cancers than the Loire countries. The complete study written by Solenne Delacour, Anne Cowppli-Bony, amd Florence Molinié, is quite cautious about the reasons for this higher rate, even using a Bayesian Poisson-Gamma smoothing (and the R package empbaysmooth), and citing the 1991 paper by Besag, York and Mollié, but the local and national medias are quick to blame the local industries for the difference. The graph above is particularly bad in that it accumulates mortality causes that are not mutually exclusive or independent. For instance, the much higher mortality rate due to alcohol is obviously responsible for higher rates of most other entries. And indicates a sociological pattern that may or may not be due to the type of job in the area, but differs from the more rural other parts of the Loire countries. (Which, like Brittany, are already significantly above (50%) the national reference for alcohol related health issues.), and may not be strongly connected to exposition to chemicals. For instance, the rates of pulmonary cancers are mostly comparable to the national average, if higher than the rest of the Loire countries and connect with a high smoking propensity. Lymphomas are not significantly different from the regional reference. The only type of cancer that can be directly attributed to working conditions are the mesothelioma, mostly caused by asbestos exposure, which was used in ship building, a specialty of the area. Among the many possible reasons for the higher mortality of the county, the study mentions a lower exposure to medical testings (connected with the sociological composition of the area). Which would indicate the most effective policies for lowering these higher cancer and mortality rates.

## Archive for Julian Besag

## poor statistics

Posted in Books, pictures, R, Statistics, Travel, Wines with tags alcoholism, Bretagne, Brittany, cancer, drugs, empbaysmooth, epidemiology, Julian Besag, Loire, Loire countries, R, R package, Saint-Nazaire on September 24, 2019 by xi'an## amazing appendix

Posted in Books, Statistics, Travel, University life with tags auxiliary variable, Colorado, Fort Collins, Gibbs sampler, Julian Besag, MCMC, Metropolis-within-Gibbs algorithm, Monte Carlo Statistical Methods, Oxford, random simulation, simulation, Statistical Science on February 13, 2018 by xi'an**I**n the first appendix of the 1995 Statistical Science paper of Besag, Green, Higdon and Mengersen, on MCMC, “Bayesian Computation and Stochastic Systems”, stands a fairly neat result I was not aware of (and which Arnaud Doucet, with his unrivalled knowledge of the literature!, pointed out to me in Oxford, avoiding me the tedium to try to prove it afresco!). I remember well reading a version of the paper in Fort Collins, Colorado, in 1993 (I think!) but nothing about this result.

It goes as follows: when running a Metropolis-within-Gibbs sampler for component x¹ of a collection of variates x¹,x²,…, thus aiming at simulating from the full conditional of x¹ given x⁻¹ by making a proposal q(x|x¹,x⁻¹), it is perfectly acceptable to use a proposal that depends on a parameter α (no surprise so far!) *and* to generate this parameter α anew at each iteration (still unsurprising as α can be taken as an auxiliary variable) *and* to have the distribution of this parameter α depending on the other variates x²,…, i.e., x⁻¹. This is the surprising part, as adding α as an auxiliary variable was messing up the update of x⁻¹. But the proof as found in the 1995 paper [page 35] does not require to consider α as such as it establishes global balance directly. (Or maybe still detailed balance when writing the whole Gibbs sampler as a cycle of Metropolis steps.) Terrific! And a whiff mysterious..!

## Gibbs for kidds

Posted in Books, Kids, Statistics, University life with tags Aarhus, animal breeder, auto-exponential model, Bath, convergence of Gibbs samplers, cross validated, Denmark, George Casella, Gibbs for Kids, Gibbs for pigs, Gibbs sampling, irreducibility, Julian Besag, Markov chains, recurrence, The American Statistician 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

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.)

## Wilfred Keith Hastings [1930-2016]

Posted in Books, Mountains, pictures, Statistics, Travel, University life with tags Bell Labs, Biometrika, Canada, Julian Besag, Metropolis-Hastings algorithm, obituary, Peskun ordering, University of Canterbury, University of Victoria, Victoria, Wilfred Keith Hastings on December 9, 2016 by xi'an**A** few days ago I found on the page Jeff Rosenthal has dedicated to Hastings that he has passed away peacefully on May 13, 2016 in Victoria, British Columbia, where he lived for 45 years as a professor at the University of Victoria. After holding positions at University of Toronto, University of Canterbury (New Zealand), and Bell Labs (New Jersey). As pointed out by Jeff, Hastings’ main paper is his 1970 Biometrika description of Markov chain Monte Carlo methods, Monte Carlo sampling methods using Markov chains and their applications. Which would take close to twenty years to become known to the statistics world at large, although you can trace a path through Peskun (his only PhD student) , Besag and others. I am sorry it took so long to come to my knowledge and also sorry it apparently went unnoticed by most of the computational statistics community.

## no thesis no more?!

Posted in Kids, University life with tags defense, Julian Besag, Nature, PhD thesis on August 5, 2016 by xi'an

“The traditional goal is to demonstrate the candidate’s ability to conduct independent research on a novel concept and to communicate the results in an accessible way. Where the academics differ is on how best to achieve that goal.”

Nature had an editorial and more on the changing nature of the PhD thesis and the possible abandonment of the thing. This is an interesting if radical proposal. There are many cases of highly successful research careers that bypassed the PhD station. Take for instance Julian Besag. On the one hand, what matters most for granting a PhD is the ability to produce independent research that is innovative enough. For this purpose, publication in a serious scientific journal is the right filter. (Serious as opposed to predatory.) Asking referees to review a thesis when the chapters have been published and hence refereed sounds like a waste of time. Nature also mentions the issue of the oral defence, which varies a lot across countries and institutions from inexistent to highly formal. If the relevance of the oral defence is to assess the ability of the candidate to present one’s work in an understandable manner, conferences should do. Except that talks are never assessed. If a speaker is poor, he or she may not get invited again by those who attended the talk. May. But this is somewhat secondary in that examples abound of geniuses who were or are unable to deliver good lectures, with no consequence on the quality of their research and collaborations. Collaborations is actually a sensitive aspect, as more and more papers that make the PhD thesis are written jointly. Evaluations of the contribution of the PhD candidate then get delicate, especially when several PhDs are involved. (I used to refrain from co-signing publications with my students during their thesis, but I have loosened this rule in the past years as I find myself more involved in some projects and hence more eager or impatient to see the outcome completed!)

On the other hand, a PhD thesis may help in getting students to focus on broader issues, when compared with published short papers on marginal improvements in quick succession. But this may not be enough of an incentive. The status of the PhD student is also somewhat unique and provides a buffer between studies and research position, where the student gradually morphs into a researcher (or gives up). If we were to abandon the PhD thesis, there would need to be some equivalent structure to give them status and financial support. However, most places accommodate graduate researchers and the ability to support them for variable periods. It would just mean adjusting for longer durations and some degree of protection…

*[The above picture is copied from the site theses.fr that compiles theses published in France and produces some basic statistics, which are all wrong in my case!]*