21w5107 [½day 4]

Final ½ day of the 21w5107 workshop for me, as our initial plans were to stop today due to the small number of participants on site. And I had booked plane tickets early, too early. I will thus sadly miss the four afternoon talks, mea culpa! However I did attend Noiritt Chandra’s talk on Bayesian factor analysis. Which has always been a bit of a mystery to me in the sense that the number q of factors need be specified, which is a prior input one rarely controls. Here the goal is to estimate a covariance matrix with a sparse representation. And q is estimated by empirical likelihood ahead of the estimation of the matrix. The focus was on minimaxity and MCMC implementation rather than objective Bayes per se! Then, Daniele Durante spoke about analytical posteriors for probit models using unified skew-Normal priors (following a 2019 Biometrika paper). Including marginal posteriors and marginal likelihood. And for various extensions like dynamic probit models. Opening other computational issues such as simulating high dimensional truncated Normal distributions. (Potential use of delayed acceptance there?) This second talk was also drifting away from objective Bayes! In the first half of his talk, Filippo Ascolani introduced us to trees of random probability measures, each mother node being the distribution of the atoms of the children nodes. (Interestingly, Kingman is both connected to (coalescent) trees and to completely random measures.) My naïve first impression was that the distributions would get more and more degenerate as the number of levels in the tree would increase, however I am unsure this is correct as Filippo mentioned getting observations on all nodes. The talk also made me wonder at how this could be related Radford Neal’s Dirichlet trees. (Which I discovered at my first ICMS workshop about 20 years ago.) Yang Ni concluded the morning with a talk on causality that provided (to me) a very smooth (re)introduction to Bayesian causal graphs.

Even more than last time, I enormously enjoyed the workshop, its location, the fantastic staff at the hotel, and the reconnection with dear friends!, just regretting we could not be a few more. I appreciate the efforts made by on-line participants to stay connected and intervene (thanks, Ed!), but the quality of interactions is sadly of another magnitude when spending all our time together. Hopefully there will be a next time and hopefully we’ll then be back to larger size (and hopefully the location will remain the same). Hasta luego, Oaxaca!

on Astra and clots

A tribune this morning in The Guardian by David Spiegelhalter on having no evidence that the Oxford/AstraZeneca vaccine causes blood clots.

“It’s a common human tendency to attribute a causal effect between different events, even when there isn’t one present: we wash the car and the next day a bird relieves itself all over the bonnet. Typical.”

David sets the 30 throboembolic events among the 5 million people vaccinated with AstraZeneca in perpective of the expected 100 deep vein thromboses a week within such a population. Which coincides with the UK’s Medicines and Healthcare Products Regulatory Agency statement that the blood clots are in par with the expected numbers in the vaccinated population. (The part of the tribune about the yellow card reports, based on 10 million vaccinated people, reiterates the remark but may prove confusing to some!) As for hoping for a rational approach to the issue,  … we would need a different type of vaccine, far from being available! As demonstrated by the decision to temporarily stop vaccinating with this vaccine, causing sure additional deaths in the coming weeks.

“Will we ever be able to resist the urge to find causal relationships between different events? One way of doing this would be promoting the scientific method and ensuring everyone understands this basic principle. Testing a hypothesis helps us see which hunches or assumptions are correct and which aren’t. In this way, randomised trials have proved the effectiveness of some Covid treatments and saved vast numbers of lives, while also showing us that some overblown claims about treatments for Covid-19, such as hydroxychloroquine and convalescent plasma, were incorrect.”

Bayesian basics in Le Monde

[The Art of] Regression and other stories

CoI: Andrew sent me this new book [scheduled for 23 July on amazon] of his with Jennifer Hill and Aki Vehtari. Which I read in my garden over a few sunny morns. And as Andrew and Aki are good friends on mine, this review is definitely subjective and biased! Hence to take with a spoonful of salt.

The “other stories’ in the title is a very nice touch. And a clever idea. As the construction of regression models comes as a story to tell, from gathering and checking the data, to choosing the model specifications, to analysing the output and setting the safety lines on its interpretation and usages. I added “The Art of” in my own title as the exercise sounds very much like an art and very little like a technical or even less mathematical practice. Even though the call to the resident stat_glm R function is ubiquitous.

The style itself is very story-like, very far from a mathematical statistics book as, e.g., C.R. Rao’s Linear Statistical Inference and Its Applications. Or his earlier Linear Models which I got while drafted in the Navy. While this makes the “Stories” part most relevant, I also wonder how I could teach from this book to my own undergrad students without acquiring first (myself) the massive expertise represented by the opinions and advice on what is correct and what is not in constructing and analysing linear and generalised linear models. In the sense that I would find justifying or explaining opinionated sentences an amathematical challenge. On the other hand, it would make for a great remote course material, leading the students through the many chapters and letting them experiment with the code provided therein, creating new datasets and checking modelling assumptions. The debate between Bayesian and likelihood solutions is quite muted, with a recommendation for weakly informative priors superseded by the call for exploring the impact of one’s assumption. (Although the horseshoe prior makes an appearance, p.209!) The chapter on math and probability is somewhat superfluous as I hardly fathom a reader entering this book without a certain amount of math and stats background. (While the book warns about over-trusting bootstrap outcomes, I find the description in the Simulation chapter a wee bit too vague.) The final chapters about causal inference are quite impressive in their coverage but clearly require a significant amount of investment from the reader to truly ingest these 110 pages.

“One thing that can be confusing in statistics is that similar analyses can be performed in different ways.” (p.121)

Unsurprisingly, the authors warn the reader about simplistic and unquestioning usages of linear models and software, with a particularly strong warning about significance. (Remember Abandon Statistical Significance?!) And keep (rightly) arguing about the importance of fake data comparisons (although this can be overly confident at times). Great Chapter 11 on assumptions, diagnostics and model evaluation. And terrific Appendix B on 10 pieces of advice for improving one’s regression model. Although there are two or three pages on the topic, at the very end, I would have also appreciated a more balanced and constructive coverage of machine learning as it remains a form of regression, which can be evaluated by simulation of fake data and assessed by X validation, hence quite within the range of the book.

The document reads quite well, even pleasantly once one is over the shock at the limited amount of math formulas!, my only grumble being a terrible handwritten graph for building copters(Figure 1.9) and the numerous and sometimes gigantic square root symbols throughout the book. At a more meaningful level, it may feel as somewhat US centric, at least given the large fraction of examples dedicated to US elections. (Even though restating the precise predictions made by decent models on the eve of the 2016 election is worthwhile.) The Oscar for the best section title goes to “Cockroaches and the zero-inflated negative binomial model” (p.248)! But overall this is a very modern, stats centred, engaging and careful book on the most common tool of statistical modelling! More stories to come maybe?!

the paper where you are a node

Sophie Donnet pointed out to me this arXived paper by Tianxi Li, Elizaveta Levina, and Ji Zhu, on a network resampling strategy for X validation, where I appear as a datapoint rather than as a [direct] citation! Which reminded me of the “where you are the hero” gamebooks with which my kids briefly played, before computer games took over. The model selection method is illustrated on a dataset made of X citations [reduced to 706 authors]  in all papers published between 2003 and 2012 in the Annals of Statistics, Biometrika, JASA, and JRSS Series B. With the outcome being the determination of a number of communities, 20, which the authors labelled as they wanted, based on 10 authors with the largest number of citations in the category. As it happens, I appear in the list, within the “mixed (causality + theory + Bayesian)” category (!), along with Jamie Robbins, Paul Fearnhead, Gilles Blanchard, Zhiqiang Tan, Stijn Vansteelandt, Nancy Reid, Jae Kwang Kim, Tyler VanderWeele, and Scott Sisson, which is somewhat mind-boggling in that I am pretty sure I never quoted six of these authors [although I find it hilarious that Jamie appears in the category, given that we almost got into a car crash together, at one of the Valencià meetings!].