Don Fraser (1925-2020)

I just received the very sad news that Don Fraser, emeritus professor of statistics at the University of Toronto, passed away this Monday, 21 December 2020. He was a giant of the field, with a unique ability for abstract modelling and he certainly pushed fiducial statistics much further than Fisher ever did. He also developed a theory of structural  inference that came close to objective Bayesian statistics, although he remained quite critical of the Bayesian approach (always in a most gentle manner, as he was a very nice man!). And most significantly contributed to high order asymptotics, to the critical analysis of ancilarity and sufficiency principles, and more beyond. (Statistical Science published a conversation with Don, in 2004, providing more personal views on his career till then.) I met with Don and Nancy rather regularly over the years, as they often attended and talked at (objective) Bayesian meetings, from the 1999 edition in Granada, to the last one in Warwick in 2019. I also remember a most enjoyable barbecue together, along with Ivar Ekeland and his family, during JSM 2018, on Jericho Park Beach, with a magnificent sunset over the Burrard Inlet. Farewell, Don!

reading classics (#4,5,6)

This week, thanks to a lack of clear instructions (from me) to my students in the Reading Classics student seminar, four students showed up with a presentation! Since I had planned for two teaching blocks, three of them managed to fit within the three hours, while the last one nicely accepted to wait till next week to present a paper by David Cox…

The first paper discussed therein was A new look at the statistical model identification, written in 1974 by Hirotugu Akaike. And presenting the AIC criterion. My student Rozan asked to give the presentation in French as he struggled with English, but it was still a challenge for him and he ended up being too close to the paper to provide a proper perspective on why AIC is written the way it is and why it is (potentially) relevant for model selection. And why it is not such a definitive answer to the model selection problem. This is not the simplest paper in the list, to be sure, but some intuition could have been built from the linear model, rather than producing the case of an ARMA(p,q) model without much explanation. (I actually wonder why the penalty for this model is (p+q)/T, rather than (p+q+1)/T for the additional variance parameter.) Or simulation ran on the performances of AIC versus other xIC’s…

The second paper was another classic, the original GLM paper by John Nelder and his coauthor Wedderburn, published in 1972 in Series B. A slightly easier paper, in that the notion of a generalised linear model is presented therein, with mathematical properties linking the (conditional) mean of the observation with the parameters and several examples that could be discussed. Plus having the book as a backup. My student Ysé did a reasonable job in presenting the concepts, but she would have benefited from this extra-week in including properly the computations she ran in R around the glm() function… (The definition of the deviance was somehow deficient, although this led to a small discussion during the class as to how the analysis of deviance was extending the then flourishing analysis of variance.) In the generic definition of the generalised linear models, I was also reminded of the
generality of the nuisance parameter modelling, which made the part of interest appear as an exponential shift on the original (nuisance) density.

The third paper, presented by Bong, was yet another classic, namely the FDR paper, Controlling the false discovery rate, of Benjamini and Hochberg in Series B (which was recently promoted to the should-have-been-a-Read-Paper category by the RSS Research Committee and discussed at the Annual RSS Conference in Edinburgh four years ago, as well as published in Series B). This 2010 discussion would actually have been a good start to discuss the paper in class, but Bong was not aware of it and mentioned earlier papers extending the 1995 classic. She gave a decent presentation of the problem and of the solution of Benjamini and Hochberg but I wonder how much of the novelty of the concept the class grasped. (I presume everyone was getting tired by then as I was the only one asking questions.) The slides somewhat made it look too much like a simulation experiment… (Unsurprisingly, the presentation did not include any Bayesian perspective on the approach, even though they are quite natural and emerged very quickly once the paper was published. I remember for instance the Valencia 7 meeting in Teneriffe where Larry Wasserman discussed about the Bayesian-frequentist agreement in multiple testing.)

Death sequence

August is not looking kindly at statisticians as I have now learned (after ten days of disconnection) of both Arnold Zellner and John Nelder passing away, on Aug. 11 and 15, respectively. Following this close the death of Julian Besag, this is a sad series of departures of leading figures in the fields of statistics and econometrics. Arnold was 83 and, although I had met him in several Valencia meetings—including one in Alicante where we sat together for breakfast with Persi Diaconis and  where an irate [and well-known ] statistician came to Arnold demanding apologies about comments made late the night before!—, I only had true interactions with him during the past years, over the Jeffreys reassessment I conducted with Judith Rousseau and Nicolas Chopin. On this occasion, Arnold was very kindly helpful, pointing out the volume that he had edited on Jeffreys and that I overlooked, discussing more philosophical points about the early part of Theory of Probability, and making a very nice overview of it at the O’Bayes 09 meeting. Always in the kindest manner. Sid Chib wrote an obituary of Arnold Zellner on the ISBA website (Arnold was the first ISBA president). Andrew Gelman also wrote some personal recollections about Arnold. A memorial site has been set up in his honour.

John Nelder was regularly attending the Read Paper sessions at the RSS and these are the only times I met him. He was an impressive figure in many ways, first and foremost for his monumental Generalised Linear Models with Peter McCullagh, a (difficult and uncompromising) book that I strongly recommend to (i.e. force upon!) my PhD students for its depth. I also remember being quite intimidated the first time I talked with him, failing to understand his arguments so completely that I dreaded later discussions… John Nelder was at  Fisher’s Rothamsted Experimental Station for most of his career and was certainly one of the last genuine Fisherians (despite a fairly rude letter of Fisher to him!).