**I**n my latest book review for CHANCE, I published my review of Michèle Audin’s Une Vie Brève. However, for a reason I cannot remember, I (?) added that the translated edition of the book was One Hundred Twenty-One Days, which is an altogether different book by the same author! (I actually cannot find a trace of this reference in my submitted LaTeX file, although this does not signify I did not add the remark when I got the proofs.) This was pointed out by the translator, Christiana Hills, so apologies to the author and to the readers for this confusion!

## Archive for CHANCE

## lost in translation [oops]

Posted in Statistics with tags book review, CHANCE, Maurice Audin, Michèle Audin, One Hundred Twenty-One Days, translation, Une Vie Brève on April 20, 2017 by xi'an## truth or truthiness [book review]

Posted in Books, Kids, pictures, Statistics, University life with tags Andrew Gelman, Cambridge University Press, causality, CHANCE, data science, Don Rubin, fracking, Howard Wainer, Oklahoma, testing, tribune, truthiness, University of Warwick on March 21, 2017 by xi'an**T**his 2016 book by Howard Wainer has been sitting (!) on my desk for quite a while and it took a long visit to Warwick to find a free spot to quickly read it and write my impressions. The subtitle is, as shown on the picture, *“Distinguishing fact from fiction by learning to think like a data scientist”*. With all due respect to the book, which illustrates quite pleasantly the dangers of (pseudo-)data mis- or over- (or eve under-)interpretation, and to the author, who has repeatedly emphasised those points in his books and ~~tribunes~~ opinion columns, including those in CHANCE, I do not think the book teaches how to think like a data scientist. In that an arbitrary neophyte reader would not manage to handle a realistic data centric situation without deeper training. But this collection of essays, some of which were tribunes, makes for a nice reading nonetheless.

I presume that in this post-truth and alternative facts [dark] era, the notion of *truthiness* is familiar to most readers! It is often based on a misunderstanding or a misappropriation of data leading to dubious and unfounded conclusions. The book runs through dozens of examples (some of them quite short and mostly appealing to common sense) to show how this happens and to some extent how this can be countered. If not avoided as people will always try to bend, willingly or not, the data to their conclusion.

There are several parts and several themes in Truth or Truthiness, with different degrees of depth and novelty. The more involved part is in my opinion the one about causality, with illustrations in educational testing, psychology, and medical trials. (The illustration about fracking and the resulting impact on Oklahoma earthquakes should not be in the book, except that there exist officials publicly denying the facts. The same remark applies to the testing cheat controversy, which would be laughable had not someone ended up the victim!) The section on graphical representation and data communication is less exciting, presumably because it comes *after* Tufte’s books and message. I also feel the 1854 cholera map of John Snow is somewhat over-exploited, since he only drew the map after the epidemic declined. The final chapter * Don’t Try this at Home* is quite anecdotal and at the same time this may the whole point, namely that in mundane questions thinking like a data scientist is feasible and leads to sometimes surprising conclusions!

*“In the past a theory could get by on its beauty; in the modern world, a successful theory has to work for a living.” (p.40)*

The book reads quite nicely, as a whole and a collection of pieces, from which class and talk illustrations can be borrowed. I like the “learned” tone of it, with plenty of citations and witticisms, some in Latin, Yiddish and even French. (Even though the later is somewhat inaccurate! *Si ça avait pu se produire, ça avait dû se produire* [p.152] would have sounded more vernacular in my Gallic opinion!) I thus enjoyed unreservedly Truth or Truthiness, for its rich style and critical message, all the more needed in the current times, and far from comparing it with a bag of potato chips as Andrew Gelman did, I would like to stress its classical tone, in the sense of being immersed in a broad and deep culture that seems to be receding fast.

## a concise introduction to statistical inference [book review]

Posted in Statistics with tags A concise introduction to statistical inference, Bayesian inference, book review, calculus, CHANCE, CRC Press, hypothesis testing, introductory textbooks, Jacco Thijssen, Riemann integration, subjective probability on February 16, 2017 by xi'an*[Just to warn readers and avoid emails about Xi’an plagiarising Christian!, this book was sent to me by CRC Press for a review. To be published in CHANCE.]*

**T**his is an introduction to statistical inference. And with 180 pages, it indeed is concise! I could actually stop the review at this point as a concise review of a concise introduction to statistical inference, as I do not find much originality in this introduction, intended for “mathematically sophisticated first-time student of statistics”. Although sophistication is in the eye of the sophist, of course, as this book has margin symbols in the guise of integrals to warn of section using “differential or integral calculus” and a remark that the book is still accessible without calculus… (Integral calculus as in Riemann integrals, not Lebesgue integrals, mind you!) It even includes appendices with the Greek alphabet, summation notations, and exponential/logarithms.

“In statistics we often bypass the probability model altogether and simply specify the random variable directly. In fact, there is a result (that we won’t cover in detail) that tells us that, for any random variable, we can find an appropriate probability model.” (p.17)

Given its limited mathematical requirements, the book does not get very far in the probabilistic background of statistics methods, which makes the corresponding chapter not particularly helpful as opposed to a prerequisite on probability basics. Since not much can be proven without “all that complicated stuff about for any ε>0” (p.29). And makes defining correctly notions like the Central Limit Theorem impossible. For instance, Chebychev’s inequality comes within a list of admitted results. There is no major mistake in the chapter, even though mentioning that two correlated Normal variables are jointly Normal (p.27) is inexact.

“The power of a test is the probability that you do not reject a null that is in fact correct.” (p.120)

Most of the book follows the same pattern as other textbooks at that level, covering inference on a mean and a probability, confidence intervals, hypothesis testing, p-values, and linear regression. With some words of caution about the interpretation of p-values. (And the unfortunate inversion of the interpretation of power above.) Even mentioning the Cult [of Significance] I reviewed a while ago.

Given all that, the final chapter comes as a surprise, being about Bayesian inference! Which should make me rejoice, obviously, but I remain skeptical of introducing the concept to readers with so little mathematical background. And hence a very shaky understanding of a notion like conditional distributions. (Which reminds me of repeated occurrences on X validated when newcomers hope to bypass textbooks and courses to grasp the meaning of posteriors and such. Like when asking why Bayes Theorem does not apply for expectations.) I can feel the enthusiasm of the author for this perspective and it may diffuse to some readers, but apart from being aware of the approach, I wonder how much they carry away from this brief (decent) exposure. The chapter borrows from Lee (2012, 4th edition) and from Berger (1985) for the decision-theoretic part. The limitations of the exercise are shown for hypothesis testing (or comparison) by the need to restrict the parameter space to two possible values. And for decision making. Similarly, introducing improper priors and *the likelihood principle* [distinguished there from *the law of likelihood*] is likely to get over the head of most readers and clashes with the level of the previous chapters. (And I do not think this is the most efficient way to argue in favour of a Bayesian approach to the problem of statistical inference: I have now dropped all references to the likelihood principle from my lectures. Not because of the controversy, but simply because the students do not get it.) By the end of the chapter, it is unclear a neophyte would be able to spell out how one could specify a prior for one of the problems processed in the earlier chapters. The appendix on de Finetti’s formalism on personal probabilities is very much unlikely to help in this regard. While it sounds so far beyond the level of the remainder of the book.

## Statistical rethinking [book review]

Posted in Books, Kids, R, Statistics, University life with tags Amazon, Bayes theorem, Bayesian data analysis, Bayesian Essentials with R, book review, CHANCE, code, convergence diagnostics, E.T. Jaynes, generalised linear models, golem, maths, matrix algebra, MCMC algorithms, mixtures of distributions, Monte Carlo Statistical Methods, Prague, R, robots, STAN, statistical modelling, Statistical rethinking on April 6, 2016 by xi'anStatistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and [rightly so!] enthusiastically recommended by Rasmus Bååth on Amazon, here are the reasons why I am quite impressed by Statistical Rethinking!

“Make no mistake: you will wreck Prague eventually.” (p.10)

While the book has a lot in common with Bayesian Data Analysis, from being in the same CRC series to adopting a pragmatic and weakly informative approach to Bayesian analysis, to supporting the use of STAN, it also nicely develops its own ecosystem and idiosyncrasies, with a noticeable Jaynesian bent. To start with, I like the highly personal style with clear attempts to make the concepts memorable for students by resorting to external concepts. The best example is the call to the myth of the golem in the first chapter, which McElreath uses as an warning for the use of statistical models (which almost are anagrams to golems!). Golems and models [and robots, another concept invented in Prague!] are man-made devices that strive to accomplish the goal set to them without heeding the consequences of their actions. This first chapter of Statistical Rethinking is setting the ground for the rest of the book and gets quite philosophical (albeit in a readable way!) as a result. In particular, there is a most coherent call against hypothesis testing, which by itself justifies the title of the book. Continue reading

## expectation-propagation from Les Houches

Posted in Books, Mountains, pictures, Statistics, University life with tags belief propagation, book review, Chamonix, CHANCE, expectation-propagation, French Alps, Lasso, Les Houches, Oxford University Press, sparsity, summer school on February 3, 2016 by xi'an**A**s CHANCE book editor, I received the other day from Oxford University Press acts from an École de Physique des Houches on Statistical Physics, Optimisation, Inference, and Message-Passing Algorithms that took place there in September 30 – October 11, 2013. While it is mostly unrelated with Statistics, and since Igor Caron already reviewed the book a year and more ago, I skimmed through the few chapters connected to my interest, from Devavrat Shah’s chapter on graphical models and belief propagation, to Andrea Montanari‘s denoising and sparse regression, including LASSO, and only read in some detail Manfred Opper’s expectation propagation chapter. This paper made me realise (or re-realise as I had presumably forgotten an earlier explanation!) that expectation propagation can be seen as a sort of variational approximation that produces by a sequence of iterations the distribution within a certain parametric (exponential) family that is the closest to the distribution of interest. By writing the Kullback-Leibler divergence the opposite way from the usual variational approximation, the solution equates the expectation of the natural sufficient statistic under both models… Another interesting aspect of this chapter is the connection with estimating normalising constants. (I noticed a slight typo on p.269 in the final form of the Kullback approximation q() to p().

## Mathematical underpinnings of Analytics (theory and applications)

Posted in Books, Statistics, University life with tags An Essay towards solving a Problem in the Doctrine of Chances, analytics, Bayes factor, Bayesian Analysis, book review, bootstrap, CHANCE, Friedrich Nietzsche, genetic algorithm, Laplace succession rule, logistic regression, machine learning, particle filter, Patti Smith, The Bayesian Choice, Yogi Berra on September 25, 2015 by xi'an

“Today, a week or two spent reading Jaynes’ book can be a life-changing experience.” (p.8)

**I** received this book by Peter Grindrod, Mathematical underpinnings of Analytics (theory and applications), from Oxford University Press, quite a while ago. (Not that long ago since the book got published in 2015.) As a book for review for CHANCE. And let it sit on my desk and in my travel bag for the same while as it was unclear to me that it was connected with Statistics and CHANCE. What is [are?!] *analytics*?! I did not find much of a definition of *analytics* when I at last opened the book, and even less mentions of statistics or machine-learning, but Wikipedia told me the following:

“Analytics is a multidimensional discipline. There is extensive use of mathematics and statistics, the use of descriptive techniques and predictive models to gain valuable knowledge from data—data analysis. The insights from data are used to recommend action or to guide decision making rooted in business context. Thus, analytics is not so much concerned with individual analyses or analysis steps, but with the entire methodology.”

Barring the absurdity of speaking of a “multidimensional discipline” [and even worse of linking with the mathematical notion of dimension!], this tells me analytics is a mix of data analysis and decision making. Hence relying on (some) statistics. Fine.

“Perhaps in ten years, time, the mathematics of behavioural analytics will be common place: every mathematics department will be doing some of it.”(p.10)

First, and to start with some positive words (!), a book that quotes both Friedrich Nietzsche and Patti Smith cannot get everything wrong! (Of course, including a most likely apocryphal quote from the now late Yogi Berra does not partake from this category!) Second, from a general perspective, I feel the book meanders its way through chapters towards a higher level of statistical consciousness, from graphs to clustering, to hidden Markov models, without precisely mentioning statistics or statistical model, while insisting very much upon Bayesian procedures and Bayesian thinking. Overall, I can relate to most items mentioned in Peter Grindrod’s book, but mostly by first reconstructing the notions behind. While I personally appreciate the distanced and often ironic tone of the book, reflecting upon the author’s experience in retail modelling, I am thus wondering at which audience Mathematical underpinnings of Analytics aims, for a practitioner would have a hard time jumping the gap between the concepts exposed therein and one’s practice, while a theoretician would require more formal and deeper entries on the topics broached by the book. I just doubt this entry will be enough to lead maths departments to adopt behavioural analytics as part of their curriculum… Continue reading

## Measuring statistical evidence using relative belief [book review]

Posted in Books, Statistics, University life with tags ABC, Bayes factor, CHANCE, CRC Press, discrepancies, Error and Inference, improper prior, integrated likelihood, Jeffreys-Lindley paradox, Likelihood Principle, marginalisation paradoxes, model checking, model validation, Monty Hall problem, Murray Aitkin, p-value, point null hypotheses, relative belief ratio, University of Toronto on July 22, 2015 by xi'an

“It is necessary to be vigilant to ensure that attempts to be mathematically general do not lead us to introduce absurdities into discussions of inference.” (p.8)

**T**his new book by Michael Evans (Toronto) summarises his views on statistical evidence (expanded in a large number of papers), which are a quite unique mix of Bayesian principles and less-Bayesian methodologies. I am quite glad I could receive a version of the book before it was published by CRC Press, thanks to Rob Carver (and Keith O’Rourke for warning me about it).* [Warning: this is a rather long review and post, so readers may chose to opt out now!]*

“The Bayes factor does not behave appropriately as a measure of belief, but it does behave appropriately as a measure of evidence.” (p.87)