statistical modeling with R [book review]

Statistical Modeling with R (A dual frequentist and Bayesian approach for life scientists) is a recent book written by Pablo Inchausti, from Uruguay. In a highly personal and congenial style (witness the preface), with references to (fiction) books that enticed me to buy them. The book was sent to me by the JASA book editor for review and I went through the whole of it during my flight back from Jeddah. [Disclaimer about potential self-plagiarism: this post or a likely edited version of it will eventually appear in JASA. If not CHANCE, for once.]

The very first sentence (after the preface) quotes my late friend Steve Fienberg, which is definitely starting on the right foot. The exposition of the motivations for writing the book is quite convincing, with more emphasis than usual put on the notion and limitations of modeling. The discourse is overall inspirational and contains many relevant remarks and links that make it worth reading it as a whole. While heavily connected with a few R packages like fitdist, fitistrplus, brms (a  front for Stan), glm, glmer, the book is wisely bypassing the perilous reef of recalling R bases. Similarly for the foundations of probability and statistics. While lacking in formal definitions, in my opinion, it reads well enough to somehow compensate for this very lack. I also appreciate the coherent and throughout continuation of the parallel description of Bayesian and non-Bayesian analyses, an attempt that often too often quickly disappear in other books. (As an aside, note that hardly anyone claims to be a frequentist, except maybe Deborah Mayo.) A new model is almost invariably backed by a new dataset, if a few being somewhat inappropriate as in the mammal sleep patterns of Chapter 5. Or in Fig. 6.1.

Given that the main motivation for the book (when compared with references like BDA) is heavily towards the practical implementation of statistical modelling via R packages, it is inevitable that a large fraction of Statistical Modeling with R is spent on the analysis of R outputs, even though it sometimes feels a wee bit too heavy for yours truly.  The R screen-copies are however produced in moderate quantity and size, even though the variations in typography/fonts (at least on my copy?!) may prove confusing. Obviously the high (explosive?) distinction between regression models may eventually prove challenging for the novice reader. The specific issue of prior input (or “defining priors”) is briefly addressed in a non-chapter (p.323), although mentions are made throughout preceding chapters. I note the nice appearance of hierarchical models and experimental designs towards the end, but would have appreciated some discussions on missing topics such as time series, causality, connections with machine learning, non-parametrics, model misspecification. As an aside, I appreciated being reminded about the apocryphal nature of Ockham’s much cited quote “Pluralitas non est ponenda sine necessitate“.

Typo Jeffries found in Fig. 2.1, along with a rather sketchy representation of the history of both frequentist and Bayesian statistics. And Jon Wakefield’s book (with related purpose of presenting both versions of parametric inference) was mistakenly entered as Wakenfield’s in the bibliography file. Some repetitions occur. I do not like the use of the equivalence symbol ≈ for proportionality. And I found two occurrences of the unavoidable “the the” typo (p.174 and p.422). I also had trouble with some sentences like “long-run, hypothetical distribution of parameter estimates known as the sampling distribution” (p.27), “maximum likelihood estimates [being] sufficient” (p.28), “Jeffreys’ (1939) conjugate priors” [which were introduced by Raiffa and Schlaifer] (p.35), “A posteriori tests in frequentist models” (p.130), “exponential families [having] limited practical implications for non-statisticians” (p.190), “choice of priors being correct” (p.339), or calling MCMC sample terms “estimates” (p.42), and issues with some repetitions, missing indices for acronyms, packages, datasets, but did not bemoan the lack homework sections (beyond suggesting new datasets for analysis).

A problematic MCMC entry is found when calibrating the choice of the Metropolis-Hastings proposal towards avoiding negative values “that will generate an error when calculating the log-likelihood” (p.43) since it suggests proposed values should not exceed the support of the posterior (and indicates a poor coding of the log-likelihood!). I also find the motivation for the full conditional decomposition behind the Gibbs sampler (p.47) unnecessarily confusing. (And automatically having a Metropolis-Hastings step within Gibbs as on Fig. 3.9 brings another magnitude of confusion.) The Bayes factor section is very terse. The derivation of the Kullback-Leibler representation (7.3) as an expected log likelihood ratio seems to be missing a reference measure. Of course, seeing a detailed coverage of DIC (Section 7.4) did not suit me either, even though the issue with mixtures was alluded to (with no detail whatsoever). The Nelder presentation of the generalised linear models felt somewhat antiquated, since the addition of the scale factor a(φ) sounds over-parameterized.

But those are minor quibble in relation to a book that should attract curious minds of various background knowledge and expertise in statistics, as well as work nicely to support an enthusiastic teacher of statistical modelling. I thus recommend this book most enthusiastically.

van Dantzig seminar

prior sensitivity of the marginal likelihood

Fernando Llorente and (Madrilene) coauthors have just arXived a paper on the safe use of prior densities for Bayesian model selection. Rather than blaming the Bayes factor, or excommunicating some improper priors, they consider in this survey solutions to design “objective” priors in model selection. (Writing this post made me realised I had forgotten to arXive a recent piece I wrote on the topic, based on short courses and blog pieces, for an incoming handbook on Bayesian advance(ment)s! Soon to be corrected.)

While intrinsically interested in the topic and hence with the study, I somewhat disagree with the perspective adopted by the authors. They for instance stick to the notion that a flat prior over the parameter space is appropriate as “the maximal expression of a non-informative prior” (despite depending on the parameterisation). Over bounded sets at least, while advocating priors “with great scale parameter” otherwise. They also refer to Jeffreys (1939) priors, by which they mean estimation priors rather than testing priors. As uncovered by Susie Bayarri and Gonzalo Garcia-Donato. Considering asymptotic consistency, they state that “in the asymptotic regime, Bayesian model selection is more sensitive to the sample size D than to the prior specifications”, which I find both imprecise and confusing,  as my feeling is that the prior specification remains overly influential as the sample size increases. (In my view, consistency is a minimalist requirement, rather than “comforting”.) The argument therein that a flat prior is informative for model choice stems from the fact that the marginal likelihood goes to zero as the support of the prior goes to infinity, which may have been an earlier argument of Jeffreys’ (1939), but does not carry much weight as the property is shared by many other priors (as remarked later). Somehow, the penalisation aspect of the marginal is not exploited more deeply in the paper. In the “objective” Bayes section, they adhere to the (convenient but weakly supported) choice of a common prior on the nuisance parameters (shared by different models). Their main argument is to develop (heretic!) “data-based priors”, from Aitkin (1991, not cited) double use of the data (or setting the likelihood to the power two), all the way to the intrinsic and fractional Bayes factors of Tony O’Hagan (1995), Jim Berger and Luis Pericchi (1996), and to the expected posterior priors of Pérez and Berger (2002) on which I worked with Juan Cano and Diego Salmeròn. (While the presentation is made against a flat prior, nothing prevents the use of another reference, improper, prior.) A short section also mentions the X-validation approach(es) of Aki Vehtari and co-authors.

the many nuances of Bayesian testing [CERminar]

ISBA 2021 grand finale

Last day of ISBA (and ISB@CIRM), or maybe half-day, since there are only five groups of sessions we can attend in Mediterranean time.

My first session was one on priors for mixtures, with 162⁺ attendees at 5:15am! (well, at 11:15 Wien or Marseille time), Gertrud Malsiner-Walli distinguishing between priors on number of components [in the model] vs number of clusters [in the data], with a minor question of mine whether or not a “prior” is appropriate for a data-dependent quantity. And Deborah Dunkel presenting [very early in the US!] anchor models for fighting label switching, which reminded me of the talk she gave at the mixture session of JSM 2018 in Vancouver. (With extensions to consistency and mixtures of regression.) And Clara Grazian debating on objective priors for the number of components in a mixture [in the Sydney evening], using loss functions to build these. Overall it seems there were many talks on mixtures and clustering this year.

After the lunch break, when several ISB@CIRM were about to leave, we ran the Objective Bayes contributed session, which actually included several Stein-like minimaxity talks. Plus one by Théo Moins from the patio of CIRM, with ciccadas in the background. Incredibly chaired by my friend Gonzalo, who had a question at the ready for each and every speaker! And then the Savage Awards II session. Which ceremony is postponed till Montréal next year. And which nominees are uniformly impressive!!! The winner will only be announced in September, via the ISBA Bulletin. Missing the ISBA general assembly for a dinner in Cassis. And being back for the Bayesian optimisation session.

I would have expected more talks at the boundary of BS & ML (as well as COVID and epidemic decision making), the dearth of which should be a cause for concern if researchers at this boundary do not prioritise ISBA meetings over more generic meetings like NeurIPS… (An exception was George Papamakarios’ talk on variational autoencoders in the Savage Awards II session.)

Many many thanks to the group of students at UConn involved in setting most of the Whova site and running the support throughout the conference. It indeed went on very smoothly and provided a worthwhile substitute for the 100% on-site version. Actually, I both hope for the COVID pandemic (or at least the restrictions attached to it) to abate and for the hybrid structure of meetings to stay, along with the multiplication of mirror workshops. Being together is essential to the DNA of conferences, but travelling to a single location is not so desirable, for many reasons. Looking for ISBA 2022, a year from now, either in Montréal, Québec, or in one of the mirror sites!