Archive for Aki Vehtari

Bayesian workflow [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 8, 2026 by xi'an


“This original, thought-provoking, and transforming, book is much much more than an implementation manual for Bayesian Data Analysis, even though it shares almost the same perspective. (The first sentence of the book states that the authors’ `conceptions of statistical practice, and of Bayesian statistics, have changed over the years’.) By providing a modus vivendi for undertaking Bayesian modelling from scratch in realistic settings where models are not magicked out of the blue, the authors explicit and rationalise the many steps required by such a bottom-up modelling protocol (`not a checklist, not a cookbook’, and not a flowchart!) in real situations. The contents read very well and very smoothly, with a seamless conjunction of intuition, modelling advices, computational details, and comparison tools. While unsurprisingly Bayesian, the perspective adopted therein remains both open and inclusive, with a welcome humility about the limitations and challenges of Bayesian workflows. This book should thus appeal to and profit a wide variety of readers, as providing guidance through an extensive collection of highly detailed examples, with shared code and exercises.”

This book proposes a modus vivendi for Bayesian modelling in applied, realistic Bayesian analysis, where models are not magicked out of the blue. It thus emphases iterative model building, model checking, computational troubleshooting, and simulated-data experimentation, filling a gap that looks glaring in retrospect. It particularly targets users and developers of Stan, with code excerpts in R and Stan. It consists of four parts:

  1. background on Bayesian methods and computational tools;
  2. the Bayesian workflow proper, namely building a statistical model from its components, together with its assessment tools;
  3. the computational aspects of fitting models, diagnosing convergence and assessing calibration;
  4. case studies.

I was eagerly waiting for the book, as I knew Andrew, Aki, and Richard had been working on it for a few years. (The quote above is the blurb I wrote upon request from the publisher.)

The tenets of BaWoFlo—if I may resort to this acronym!—are (i) fitting multiple models, (ii) applying methods repeatedly, and (iii) resorting to simulated-data experiments, which should not come as a surprise to readers of BDA. As noted in the introduction, the protocol exposed therein can also benefit non-Bayesian experimenters. This agrees with the highly moderate, “M-open”, agnostic approach to Bayesianism adopted by the authors (“there is no safe haven”). I also welcome and share their humble perspective about the limitations and challenges of Bayesian workflows.

Examples are treated in full detail, with successive modelling and computational choices profusely commented, which is a big plus for such a practical book. This starts as early as Chapter 4, with a multiple-choice exam example. Indeed, there cannot be general principles or a generic theory that would make the approach foolproof. See, e.g., “A data model is not just a ‘likelihood’” (p.70), as when the data model is not fully generative. I very much liked the section on choosing priors (5.6), and the very rich graphs (see, e.g., Chapter 8) for assessing the impact of prior and likelihood, as well as for predictive checks. In coherent continuation of the authors’ earlier work, the book advocates LOO methods and model stacking rather than model averaging. (With a surprisingly anti-Ockham perspective in Section 9.7.)

The MCMC coverage is unsurprising, with \(\hat R\) at the forefront. Chapter 12, on using fast experiments to detect fitting or computational issues, is very nice. The book builds on the immense corpus of work achieved by the authors over the decades (for the most senior ones!). By contrast, the chapter on approximate solutions (13) is way too short, and the same goes for those on calibration and software development.

The book is very US-centric, unsurprisingly given Andrew’s focus on political science. Some sections are reminiscent of Andrew’s blog entries (or the opposite). The (football) World Cup example was initiated when Andrew was in France, during the 2014 World Cup, and as a result (?) the names of the teams are in French! One chapter also reanalyses the birthdate data displayed on the cover of BDA.

Mileage varies on the applied chapters, depending on the example. A dog chapter is followed by a cat chapter! Not that the (stat)dog experiment was in any way enjoyable, especially for the dogs. Maybe the cats were running it! And then come chapters on roaches and sharks. There is also a frightening flowchart (Fig. 2.1)! And the book ends with an appendix on going through BDA to better understand BaWoFlo

[The usual disclaimer applies, namely that this review is likely to appear later in CHANCE, in my book reviews column.]

Bayesian Workflow [cover]

Posted in Books, pictures, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , on April 25, 2026 by xi'an

Ah great, the new book on Bayesian workflow by Andrew Gelman, Aki Vehtari, Richard McElreath I knew they were working on is about to appear!  With entries from several coauthors and half of the chapters on case studies. I have not (yet) looked at its contents in detail…

Active Statistics: Stories, Games, Problems, and Hands-on Demonstrations [it’s out now!]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , , on March 13, 2024 by xi'an

[The Art of] Regression and other stories

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , on July 23, 2020 by xi'an

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?!

projective covariate selection

Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on October 28, 2014 by xi'an

While I was in Warwick, Dan Simpson [newly arrived from Norway on a postdoc position] mentioned to me he had attended a talk by Aki Vehtari in Norway where my early work with Jérôme Dupuis on projective priors was used. He gave me the link to this paper by Peltola, Havulinna, Salomaa and Vehtari that indeed refers to the idea that a prior on a given Euclidean space defines priors by projections on all subspaces, despite the zero measure of all those subspaces. (This notion first appeared in a joint paper with my friend Costas Goutis, who alas died in a diving accident a few months later.) The projection further allowed for a simple expression of the Kullback-Leibler deviance between the corresponding models and for a Pythagorean theorem on the additivity of the deviances between embedded models. The weakest spot of this approach of ours was, in my opinion and unsurprisingly, about deciding when a submodel was too far from the full model. The lack of explanatory power introduced therein had no absolute scale and later discussions led me to think that the bound should depend on the sample size to ensure consistency. (The recent paper by Nott and Leng that was expanding on this projection has now appeared in CSDA.)

“Specifically, the models with subsets of covariates are found by maximizing the similarity of their predictions to this reference as proposed by Dupuis and Robert [12]. Notably, this approach does not require specifying priors for the submodels and one can instead focus on building a good reference model. Dupuis and Robert (2003) suggest choosing the size of the covariate subset based on an acceptable loss of explanatory power compared to the reference model. We examine using cross-validation based estimates of predictive performance as an alternative.” T. Peltola et al.

The paper also connects with the Bayesian Lasso literature, concluding on the horseshoe prior being more informative than the Laplace prior. It applies the selection approach to identify biomarkers with predictive performances in a study of diabetic patients. The authors rank model according to their (log) predictive density at the observed data, using cross-validation to avoid exploiting the data twice. On the MCMC front, the paper implements the NUTS version of HMC with STAN.