**S**ince this teaching semester is 100% on-line in Paris Dauphine for the third year students, I started last Monday to teach my statistical modelling course from my office on my computer. Using a Teams connection with the 180⁺ students, sharing my slides *or* my webcam with them, and writing on a Huion drawing tablet to write on the pdf slides (or on Teams whiteboard). I found the most convenient way to write on the slides was via Xournalpp. From my end of the exchange, the class went on rather smoothly, with students interacting about the practical and contents of the course. As I have also recorded my lectures (in August), and hope the students to first go through the recordings, I will see next time how much effort they have put into assimilating the material, as the on-line class will mostly concentrate on questions and applications. I also hope to have a quick multiple choice question at the end (or beginning?) of each class, but am still fishing for an interface that would (a) handle LaTeX or MathJax (b) shuffle questions from a pool of questions so that each student gets a different question (or thinks so) and (c) store the outcome of the test. Any suggestion welcome!

## Archive for LaTeX

## on-line course

Posted in Kids, pictures, Statistics, University life with tags courses in English, drawing tablet, Huion, LaTeX, MathJax, multiple choice question, on-line course, pdf, questionnaire, teaching, Université Paris Dauphine, xournalpp on September 4, 2020 by xi'an## sans sérif & sans chevron

Posted in Books, R, Statistics, University life with tags bicycle, book publishing, chevron, final exam, LaTeX, mathematical statistics, multiple answer test, R, R code, sans-sérif, simulation, vélo, Zoom on June 17, 2020 by xi'an{\sf df=function(x)2*pi*x-4*(x>1)*acos(1/(x+(1-x)*(x<1)))}

**A**s I was LaTeXing a remote exam for next week, including some R code questions, I came across the apparent impossibility to use < and > symbols in the sans-sérif “\sf” font… Which is a surprise, given the ubiquity of the symbols in R and my LaTeXing books over the years. Must have always used “\tt” and “\verb” then! On the side, I tried to work with the automultiplechoice LaTeX package [which should be renamed velomultiplechoice!] of Alexis Bienvenüe, which proved a bit of a challenge as the downloadable version contained a flawed file of automultiplechoice.sty! Still managed to produce a 400 question exam with random permutations of questions and potential answers. But not looking forward the 4 or 5 hours of delivering the test on Zoom…

## Probability and Bayesian modeling [book review]

Posted in Books, Kids, R, Statistics, University life with tags baseball data, book review, CRC Press, Cross Validation, deviance information criterion, DIC, dplyr, Francis Galton, JAGS, LaTeX, measure theory, Poisson distribution, Roger Federer, sub-two-hours marathon, subjective probability, the the, unconscious statistician, weakly informative prior on March 26, 2020 by xi'anProbability and Bayesian modeling is a textbook by Jim Albert *[whose reply is included at the end of this entry]* and Jingchen Hu that CRC Press sent me for review in CHANCE. (The book is also freely available in bookdown format.) The level of the textbook is definitely most introductory as it dedicates its first half on probability concepts (with no measure theory involved), meaning mostly focusing on counting and finite sample space models. The second half moves to Bayesian inference(s) with a strong reliance on JAGS for the processing of more realistic models. And R vignettes for the simplest cases (where I discovered R commands I ignored, like dplyr::mutate()!).

As a preliminary warning about my biases, I am always reserved at mixing introductions to probability theory and to (Bayesian) statistics in the same book, as I feel they should be separated to avoid confusion. As for instance between histograms and densities, or between (theoretical) expectation and (empirical) mean. I therefore fail to relate to the pace and tone adopted in the book which, in my opinion, seems to dally on overly simple examples [far too often concerned with food or baseball] while skipping over the concepts and background theory. For instance, introducing the concept of subjective probability as early as page 6 is laudable but I doubt it will engage fresh readers when describing it as a measurement of one’s “belief about the truth of an event”, then stressing that “make any kind of measurement, one needs a tool like a scale or ruler”. Overall, I have no particularly focused criticisms on the probability part except for the discrete vs continuous imbalance. (With the Poisson distribution not covered in the Discrete Distributions chapter. And the “bell curve” making a weird and unrigorous appearance there.) Galton’s board (no mention found of quincunx) could have been better exploited towards the physical definition of a prior, following Steve Stiegler’s analysis, by adding a second level. Or turned into an R coding exercise. In the continuous distributions chapter, I would have seen the cdf coming first to the pdf, rather than the opposite. And disliked the notion that a Normal distribution was supported by an histogram of (marathon) running times, i.e. values lower bounded by 122 (at the moment). Or later (in Chapter 8) for Roger Federer’s serving times. Incidentally, a fun typo on p.191, at least fun for LaTeX users, as

with an extra space between `\’ and `mid’! (I also noticed several occurrences of the unvoidable “the the” typo in the last chapters.) The simulation from a bivariate Normal distribution hidden behind a customised R function sim_binom() when it could have been easily described as a two-stage hierarchy. And no comment on the fact that a sample from Y-1.5X could be directly derived from the joint sample. (Too unconscious a statistician?)

When moving to Bayesian inference, a large section is spent on very simple models like estimating a proportion or a mean, covering both discrete and continuous priors. And strongly focusing on conjugate priors despite giving warnings that they do not necessarily reflect prior information or prior belief. With some debatable recommendation for “large” prior variances as weakly informative or (worse) for Exp(1) as a reference prior for sample precision in the linear model (p.415). But also covering Bayesian model checking either via prior predictive (hence Bayes factors) or posterior predictive (with no mention of using the data twice). A very marginalia in introducing a sufficient statistic for the Normal model. In the Normal model checking section, an estimate of the posterior density of the mean is used without (apparent) explanation.

“It is interesting to note the strong negative correlation in these parameters. If one assigned informative independent priors on and , these prior beliefs would be counter to the correlation between the two parameters observed in the data.”

For the same reasons of having to cut on mathematical validation and rigour, Chapter 9 on MCMC is not explaining why MCMC algorithms are converging outside of the finite state space case. The proposal in the algorithmic representation is chosen as a Uniform one, since larger dimension problems are handled by either Gibbs or JAGS. The recommendations about running MCMC do not include how many iterations one “should” run (or other common queries on Stack eXchange), albeit they do include the sensible running multiple chains and comparing simulated predictive samples with the actual data as a model check. However, the MCMC chapter very quickly and inevitably turns into commented JAGS code. Which I presume would require more from the students than just reading the available code. Like JAGS manual. Chapter 10 is mostly a series of examples of Bayesian hierarchical modeling, with illustrations of the shrinkage effect like the one on the book cover. Chapter 11 covers simple linear regression with some mentions of weakly informative priors, although in a BUGS spirit of using large [enough?!] variances: “If one has little information about the location of a regression parameter, then the choice of the prior guess is not that important and one chooses a large value for the prior standard deviation . So the regression intercept and slope are each assigned a Normal prior with a mean of 0 and standard deviation equal to the large value of 100.” (p.415). Regardless of the scale of y? Standardisation is covered later in the chapter (with the use of the R function scale()) as part of constructing more informative priors, although this sounds more like data-dependent priors to me in the sense that the scale and location are summarily estimated by empirical means from the data. The above quote also strikes me as potentially confusing to the students, as it does not spell at all how to design a joint distribution on the linear regression coefficients that translate the concentration of these coefficients along y̅=β⁰+β¹x̄. Chapter 12 expands the setting to multiple regression and generalised linear models, mostly consisting of examples. It however suggests using cross-validation for model checking and then advocates DIC (deviance information criterion) as “to approximate a model’s out-of-sample predictive performance” (p.463). If only because it is covered in JAGS, the definition of the criterion being relegated to the last page of the book. Chapter 13 concludes with two case studies, the (often used) Federalist Papers analysis and a baseball career hierarchical model. Which may sound far-reaching considering the modest prerequisites the book started with.

In conclusion of this rambling [lazy Sunday] review, this is not a textbook I would have the opportunity to use in Paris-Dauphine but I can easily conceive its adoption for students with limited maths exposure. As such it offers a decent entry to the use of Bayesian modelling, supported by a specific software (JAGS), and rightly stresses the call to model checking and comparison with pseudo-observations. Provided the course is reinforced with a fair amount of computer labs and projects, the book can indeed achieve to properly introduce students to Bayesian thinking. Hopefully leading them to seek more advanced courses on the topic.

**Update:** Jim Albert sent me the following precisions after this review got on-line:

Thanks for your review of our recent book. We had a particular audience in mind, specifically undergraduate American students with some calculus background who are taking their first course in probability and statistics. The traditional approach (which I took many years ago) teaches some probability one semester and then traditional inference (focusing on unbiasedness, sampling distributions, tests and confidence intervals) in the second semester. There didn’t appear to be any Bayesian books at that calculus-based undergraduate level and that motivated the writing of this book. Anyway, I think your comments were certainly fair and we’ve already made some additions to our errata list based on your comments.

*[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about Chance!]*

## What does the symbol for pi with a lower perpendicular mean?

Posted in Books, pictures, University life with tags cross validated, indicator function, LaTeX, pi, symbol on November 1, 2019 by xi'an## natural LaTeX

Posted in Books, Statistics, University life with tags LaTeX, MathJax, Nature, StackExchange, typesetting, word processors, Word versus LaTeX on July 13, 2019 by xi'an**N**ature must have been out of inspiration in the past weeks for running a two-page article on L^{a}T_{e}X [as the toolbox column] and how it compares with… Word! Which is not so obvious since most articles in Nature are not involving equations (much) and are from fields where Word prevails. Besides the long-running whine that LaTeX is not he selling argument for this article seemed to be the increasing facility to use (basic) LaTeX commands in forums (like Stack Exchange) and blogs (like WordPress) via MathJax. But the author also pushes for the lighter (R?)Markdown as, “in LaTeX, there is a greater risk that contributors will make changes that prevent the code compiling into a PDF” (which does not make sense to me). This tribune also got me to find out that there is a blog dedicated to the “LaTeX fetish”, which sounds to me like an perfect illustration of Internet vigilantism, especially with arguments like “free and open source software has a strong tendency towards being difficult to install and get up and running”.