new arXiv rendering

arXiv is now testing a new display of papers in html format to increase accessibility [for those with no pdf reader?] Hopefully, this will not induce further constraints on the LaTeX format of arXiv submissions, at a time when it got easier for off-the-shelf files to be immediately accepted, but the fact that the site encourages using Overleaf is not that promising… (The plea that readers do not create reports that the HTML paper doesn’t look exactly like the PDF paper is hilarious, as I presume many complained of exactly this drawback.)

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.

Extending R

As I was previously unaware of this book coming up, my surprise and excitement were both extreme when I received it from CRC Press a few weeks ago! John Chambers, one of the fathers of S, precursor of R, had just published a book about extending R. It covers some reflections of the author on programming and the story of R (Parts 2 and 1),  and then focus on object-oriented programming (Part 3) and the interfaces from R to other languages (Part 4). While this is “only” a programming book, and thus not strictly appealing to statisticians, reading one of the original actors’ thoughts on the past, present, and future of R is simply fantastic!!! And John Chambers is definitely not calling to simply start over and build something better, as Ross Ihaka did in this [most read] post a few years ago. (It is also great to see the names of friends appearing at times, like Julie, Luke, and Duncan!)

“I wrote most of the original software for S3 methods, which were useful for their application, in the early 1990s.”

In the (hi)story part, Chambers delves into the details of the evolution of S at Bells Labs, as described in his [first]  “blue book” (which I kept on my shelf until very recently, next to the “white book“!) and of the occurrence of R in the mid-1990s. I find those sections fascinating maybe the more because I am somewhat of a contemporary, having first learned Fortran (and Pascal) in the mid-1980’s, before moving in the early 1990s to C (that I mostly coded as translated Pascal!), S-plus and eventually R, in conjunction with a (forced) migration from Unix to Linux, as my local computer managers abandoned Unix and mainframe in favour of some virtual Windows machines. And as I started running R on laptops with the help of friends more skilled than I (again keeping some of the early R manuals on my shelf until recently). Maybe one of the most surprising things about those reminiscences is that the very first version of R was dated Feb 29, 2000! Not because of Feb 29, 2000 (which, as Chambers points out, is the first use of the third-order correction to the Gregorian calendar, although I would have thought 1600 was the first one), but because I would have thought it appeared earlier, in conjunction with my first Linux laptop, but this memory is alas getting too vague!

As indicated above, the book is mostly about programming, which means in my case that some sections are definitely beyond my reach! For instance, reading “the onus is on the person writing the calling function to avoid using a reference object as the argument to an existing function that expects a named list” is not immediately clear… Nonetheless, most sections are readable [at my level] and enlightening about the mottoes “everything that exists is an object” and “everything that happens is a function” repeated throughout.  (And about my psycho-rigid ways of translating Pascal into every other language!) I obviously learned about new commands and notions, like the difference between

x <- 3

and

x <<- 3

(but I was disappointed to learn that the number of <‘s was not related with the depth or height of the allocation!) In particular, I found the part about replacement fascinating, explaining how a command like

diag(x)[i] = 3

could modify x directly. (While definitely worth reading, the chapter on R packages could have benefited from more details. But as Chambers points out there are whole books about this.) Overall, I am afraid the book will not improve my (limited) way of programming in R but I definitely recommend it to anyone even moderately skilled in the language.

Le Monde puzzle [#913]

An arithmetics Le Monde mathematical puzzle:

Find all bi-twin integers, namely positive integers such that adding 2 to any of their dividers returns a prime number.

An easy puzzle, once the R libraries on prime number decomposition can be found!, since it is straightforward to check for solutions. Unfortunately, I could not install the recent numbers package. So I used instead the schoolmath R package. Despite its possible bugs. But it seems to do the job for this problem:

lem=NULL
for (t in 1:1e4) 
  if (prod(is.prim(prime.factor(t)+2)==1)) 
    lem=c(lem,t)digin=function(n){

which returned all solutions, albeit in a lengthy fashion:

> lem
 [1] 1 3 5 9 11 15 17 25 27 29 33 41 45 51 55
 [16] 59 71 75 81 85 87 99 101 107 121 123 125 135 137 145
 [31] 149 153 165 177 179 187 191 197 205 213 225 227 239 243 255
 [46] 261 269 275 281 289 295 297 303 311 319 321 347 355 363 369
 [61] 375 405 411 419 425 431 435 447 451 459 461 493 495 505 521
 [76] 531 535 537 561 569 573 591 599 605 615 617 625 639 641 649
 [91] 659 675 681 685 697 717 725 729 745 765 781 783 807 809 821
[106] 825 827 841 843 857 867 881 885 891 895 909 933 935 955 957
[121] 963 985 1003 1019 1025 1031 ...