From the recently started ASA books series on statistical reasoning in science and society (of which I already reviewed a sequel to The Lady tasting Tea), a short book, Statistics and Health Care Fraud, I read at the doctor while waiting for my appointment, with no chances of cheating! While making me realise that there is a significant amount of health care fraud in the US, of which I had never though of before (!), with possibly specific statistical features to the problem, besides the use of extreme value theory, I did not find me insight there on the techniques used to detect these frauds, besides the accumulation of Florida and Texas examples. As such this is a very light introduction to the topic, whose intended audience of choice remains unclear to me. It is stopping short of making a case for statistics and modelling against more machine-learning options. And does not seem to mention false positives… That is, the inevitable occurrence of some doctors or hospitals being above the median costs! (A point I remember David Spiegelhalter making a long while ago, during a memorable French statistical meeting in Pau.) The book also illustrates the use of a free auditing software called Rat-stats for multistage sampling, which apparently does not go beyond selecting claims at random according to their amount. Without learning from past data. (I also wonder if the criminals can reduce the chances of being caught by using this software.)

A second book on the “same” topic!, Measuring Crime, I read, not waiting at the police station, but while flying to Venezia. As indicated by the title, this is about measuring crime, with a lot of emphasis on surveys and census and the potential measurement errors at different levels of surveying or censusing… Again very little on statistical methodology, apart from questioning the data, the mode of surveying, crossing different sources, and establishing the impact of the way questions are stated, but also little on bias and the impact of policing and preventing AIs, as discussed in Weapons of Math Destruction and in some of Kristin Lum’s papers.Except for the almost obligatory reference to Minority Report. The book also concludes on an history chapter centred at Edith Abbott setting the bases for serious crime data collection in the 1920’s.

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

that must have been used in so many homeworks and exam handouts by now that it should become a folk theorem. More innovative is the argument that E[1/min{X¹,X²,…}] does not exist for iid U(0,θ) because it is the minimum and thus is the only one among the order statistics with the ability to touch zero. Another universal shortcut was the completeness conclusion that when the integral

was zero for all θ’s then φ had to be equal to zero with no further argument (only one student thought to take the derivative). Plus a growing inability in the cohort to differentiate even simple functions… (At least, most students got the bootstrap right, as exemplified by their R code.) And three stars to the student who thought of completely gluing his anonymisation tag, on every one of his five sheets!, making identification indeed impossible, except by elimination of the 159 other names.

The Handbook of Mixture Analysis is now out! After a few years of planning, contacts, meetings, discussions about notations, interactions with authors, further interactions with late authors, repeating editing towards homogenisation, and a final professional edit last summer, this collection of nineteen chapters involved thirty-five contributors. I am grateful to all participants to this piece of work, especially to Sylvia Früwirth-Schnatter for being a driving force in the project and for achieving a much higher degree of homogeneity in the book than I expected. I would also like to thank Rob Calver and Lara Spieker of CRC Press for their boundless patience through the many missed deadlines and their overall support.

Two chapters which I co-authored are now available as arXived documents:

A very short book (128 pages, but with a very high price!) I received from CRC Press is Henk Tijms’ Surprises in Probability (Seventeen Short Stories).Henk Tijms is an emeritus professor of econometrics at the Vrije University in Amsterdam and he wrote these seventeen pieces either for the Dutch Statistical Society magazine or for a blog he ran for the NYt. (The video of A Night in Casablanca above is only connected to this blog through Chico mimicking the word surprise as soup+rice.)

The author mentions that the book can be useful for teachers and indeed this is a collection of surprising probability results, surprising in the sense that the numerical probabilities are not necessarily intuitive. Most illustrations involve betting of one sort or another, with only basic (combinatorial) probability distributions involved. Readers should not worry about even this basic probability background since most statements are exposed without a proof. Most examples are very classical, from the prisoner’s problem, to the Monty Hall paradox, to the birthday problem, to Benford’s distribution of digits, to gambler’s ruin, gambler’s fallacy, and the St Petersbourg paradox, to the secretary’s problem and stopping rules. The most advanced notion is the one of (finite state) Markov chains. As martingales are only mentionned in connection with pseudo-probabilist schemes for winning the lottery. For which (our very own!) Jeff Rosenthal makes an appearance, thanks to his uncovering of the Ontario Lottery scam!

“In no other branch of mathematics is it so easy for experts to blunder as in probability theory.” Martin Gardner

A few stories have entries about Bayesian statistics, with mentions made of the O.J. Simpson, Sally Clark and Lucia de Berk miscarriages of justice, although these mentions make the connection most tenuous. Simulation is also mentioned as a manner of achieving approximations to more complex probabilities. But not to the point of discussing surprises about simulation, which could have been the case with the simulation of rare events.

Ten most beautiful probability formulas (Story 10) reminded me of Ian Steward 17 formulas that changed the World. Obviously at another scale and in a much less convincing way. To wit, the Normal (or Gauss) density, Bayes’ formula, the gambler’s ruin formula, the squared-root formula (meaning standard deviation decreases as √n), Kelly’s betting formula (?), the asymptotic law of distribution of prime numbers (??), another squared-root formula for the one-dimensional random walk, the newsboy formula (?), the Pollaczek-Khintchine formula (?), and the waiting-time formula. I am not sure I would have included any of these…

All in all this is a nice if unsurprising database for illustrations and possibly exercises in elementary probability courses, although it will require some work from the instructor to link the statements to their proof. As one would expect from blog entries. But this makes for a nice reading, especially while traveling and I hope some fellow traveler will pick the book from where I left it in Mexico City airport.

The CRC Press Handbook of ABC is now out, after a rather long delay [the first version of our model choice chapter was written in 2015!] due to some late contributors Which is why I did not spot it at JSM 2018. As announced a few weeks ago, our Handbook of Mixture Analysis is soon to be published as well. (Not that I necessarily advocate the individual purchase of these costly volumes!, especially given most chapters are available on-line.)

On the occasion of my talk at JSM2018, CRC Press sent me the cover of our incoming handbook on mixture analysis, courtesy of Rob Calver who managed to get it to me on very short notice! We are about ready to send the manuscript to CRC Press and hopefully the volume will get published pretty soon. It would have been better to have it ready for JSM2018, but we editors got delayed by a few months for the usual reasons.