Hélène Massam (1949-2020)

I was much saddened to hear yesterday that our friend and fellow Bayesian Hélène Massam passed away on August 22, 2020, following a cerebrovascular accident. She was professor of Statistics at York University, in Toronto, and, as her field of excellence covered [the geometry of] exponential families, Wishart distributions and graphical models, we met many times at both Bayesian and non-Bayesian conferences  (the first time may have been an IMS in Banff, years before BIRS was created). And always had enjoyable conversations on these occasions (in French since she was born in Marseille and only moved to Canada for her graduate studies in optimisation). Beyond her fundamental contributions to exponential families, especially Wishart distributions under different constraints [including the still opened 2007 Letac-Massam conjecture], and graphical models, where she produced conjugate priors for DAGs of all sorts, she served the community in many respects, including in the initial editorial board of Bayesian Analysis. I can also personally testify of her dedication as a referee as she helped with many papers along the years. She was also a wonderful person, with a great sense of humor and a love for hiking and mountains. Her demise is a true loss for the entire community and I can only wish her to keep hiking on new planes and cones in a different dimension. [Last month, Christian Genest (McGill University) and Xin Gao (York University) wrote a moving obituary including a complete biography of Hélène for the Statistical Society of Canada.]

chain event graphs [RSS Midlands seminar]

Last evening, I attended the RSS Midlands seminar here in Warwick. The theme was chain event graphs (CEG), As I knew nothing about them, it was worth my time listening to both speakers and discussing with Jim Smith afterwards. CEGs are extensions of Bayes nets with originally many more nodes since they start with the probability tree involving all modalities of all variables. Intensive Bayesian model comparison is then used to reduce the number of nodes by merging modalities having the same children or removing variables with no impact on the variable of interest. So this is not exactly a new Bayes net based on modality dummies as nodes (my original question). This is quite interesting, esp. in the first talk illustration of using missing value indicators as a supplementary variable (to determine whether or not data is missing at random). I also wonder how much of a connection there is with variable length Markov chains (either as a model or as a way to prune the tree). A last vague idea is a potential connection with lumpable Markov chains, a concept I learned from Kemeny & Snell (1960): a finite Markov chain is lumpable if by merging two or more of its states it remains a Markov chain. I do not know if this has ever been studied from a statistical point of view, i.e. testing for lumpability, but this sounds related to the idea of merging modalities of some variables in the probability tree…

Hierarchical vs. graphical models

An email from a reader:

I’m studying your book  The Bayesian Choice (2007). I know that you mentioned graphics models in the Notes of Section 10. But I’m still confused on what is Hierarchical Bayesian Models and Graphical Models. It seems to me that Hierarchical models are just special cases of graphical models. The Bayesian network that corresponds to a graphical model is a DAG in general and the Bayesian network that corresponds to a hierarchical model is just a chain of directed edges.

Would you please take a few seconds to point me some references or discussions so that I can understand their differences better?

To which I can only reply that hierarchical models are indeed special cases of graphical models for which the edges have some kind of causal interpretation and where some conditional independence relations are imposed by the hierarchy, which is not always the case for graphical models. As probabilistic objects and as distributions, both structures belong to the same family. Inference on those objects may be different though, in that [presence or absence of] edges may be examined individually in graphical models, less so in hierarchical models where they come [and go] in batches respecting the hierarchy (see e.g. random effect models).

Anathem

One colleague of mine in Dauphine gave me Anathem to read a few weeks ago. I had seen it in a bookstore once and planned to read it, so this was a perfect opportunity. I read through it slowly at first and then with more and more eagerness as the story built on, spending a fair chunk of the past evenings (and Metro rides) into finishing it. Anathem is a wonderful book, especially for mathematicians, and while it could still qualify as a science-fiction book, it blurs the frontiers between the genres of science-fiction, speculative fiction, documentary writings and epistemology… Just imagine any other sci’fi’ book being reviewed in Nature! Still, the book was awarded the 2009 Locus SF Award. So it has true sci’fi’ characteristics, including Clarke-ian bouts of space opera with a Rama-like vessel popping out of nowhere. But this is not the main feature that makes Anathem so unique and fascinating.

“The Adrakhonic theorem, which stated that the square of a right triangle hypotenuse was equal to the sum of the squares of the other two sides…” (p. 128)

Le Monde puzzle [46]

This week puzzle in Le Monde does not make much sense, unless I miss the point: in an undirected graph with 2011 nodes, each node is linked with at least 1005 other nodes. Is there always a node that is linked with all the nodes? If I take the first two nodes, 1 and 2, if there were no common node, the 1005 nodes linked with 1 would differ from the 1005 nodes linked with 2 and would not include 2. This corresponds to 1+1005+1005+1=2012 nodes… Sounds too easy, doesn’t it?!

Update (111810): Easy, too easy! Robin pointed out to me yesterday that this proves that 1 and 2 share a neighbour, nothing more. His counterexample to the existence of a common neighbour is to create nodes from node i to any node but (i-1) mod n and (i+1) mod n, which makes a graph with n-3 edges leaving from each node and still no common neighhbour! Conclusion: I should not try to quick-solve puzzles at 4:38am…