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Bayes’ Rule [book review]

Posted in Books, Statistics, University life with tags , , , , , , , , , , on July 10, 2014 by xi'an

This introduction to Bayesian Analysis, Bayes’ Rule, was written by James Stone from the University of Sheffield, who contacted CHANCE suggesting a review of his book. I thus bought it from amazon to check the contents. And write a review.

First, the format of the book. It is a short paper of 127 pages, plus 40 pages of glossary, appendices, references and index. I eventually found the name of the publisher, Sebtel Press, but for a while thought the book was self-produced. While the LaTeX output is fine and the (Matlab) graphs readable, pictures are not of the best quality and the display editing is minimal in that there are several huge white spaces between pages. Nothing major there, obviously, it simply makes the book look like course notes, but this is in no way detrimental to its potential appeal. (I will not comment on the numerous appearances of Bayes’ alleged portrait in the book.)

“… (on average) the adjusted value θMAP is more accurate than θMLE.” (p.82)

Bayes’ Rule has the interesting feature that, in the very first chapter, after spending a rather long time on Bayes’ formula, it introduces Bayes factors (p.15).  With the somewhat confusing choice of calling the prior probabilities of hypotheses marginal probabilities. Even though they are indeed marginal given the joint, marginal is usually reserved for the sample, as in marginal likelihood. Before returning to more (binary) applications of Bayes’ formula for the rest of the chapter. The second chapter is about probability theory, which means here introducing the three axioms of probability and discussing geometric interpretations of those axioms and Bayes’ rule. Chapter 3 moves to the case of discrete random variables with more than two values, i.e. contingency tables, on which the range of probability distributions is (re-)defined and produces a new entry to Bayes’ rule. And to the MAP. Given this pattern, it is not surprising that Chapter 4 does the same for continuous parameters. The parameter of a coin flip.  This allows for discussion of uniform and reference priors. Including maximum entropy priors à la Jaynes. And bootstrap samples presented as approximating the posterior distribution under the “fairest prior”. And even two pages on standard loss functions. This chapter is followed by a short chapter dedicated to estimating a normal mean, then another short one on exploring the notion of a continuous joint (Gaussian) density.

“To some people the word Bayesian is like a red rag to a bull.” (p.119)

Bayes’ Rule concludes with a chapter entitled Bayesian wars. A rather surprising choice, given the intended audience. Which is rather bound to confuse this audience… The first part is about probabilistic ways of representing information, leading to subjective probability. The discussion goes on for a few pages to justify the use of priors but I find completely unfair the argument that because Bayes’ rule is a mathematical theorem, it “has been proven to be true”. It is indeed a maths theorem, however that does not imply that any inference based on this theorem is correct!  (A surprising parallel is Kadane’s Principles of Uncertainty with its anti-objective final chapter.)

All in all, I remain puzzled after reading Bayes’ Rule. Puzzled by the intended audience, as contrary to other books I recently reviewed, the author does not shy away from mathematical notations and concepts, even though he proceeds quite gently through the basics of probability. Therefore, potential readers need some modicum of mathematical background that some students may miss (although it actually corresponds to what my kids would have learned in high school). It could thus constitute a soft entry to Bayesian concepts, before taking a formal course on Bayesian analysis. Hence doing no harm to the perception of the field.

Chinese versus Japanese editions

Posted in Books, R, Statistics with tags , , , on March 9, 2010 by xi'an

Last week, I got news from Springer Verlag about possibly two new editions of my books, one in Chinese and one in Japanese. These were bad news and good news: the bad news was that the Chinese edition was actually a reprint of our original book,  Monte Carlo Statistical Method, by a Chinese publishing company. Supposedly restricted to the Chinese interior market. While this agreement is within the terms of our contract, it will be disastrous for our sales of the original 2004 Springer edition since those cheaper copies have already found their way to American and European markets (I got a copy by the mail only today, but some students in the US do have it!)

I actually fail to understand the publisher’s point in giving away sales of a reasonably successful book for a cheaper version with a much lower return. Since this Chinese publisher is also (re)printing Hastie, Tibshirani and Freedman’ The Elements of Statistical Learning: Data Mining, Inference, and Prediction, as well as Erich Lehmann’s Theory of Point Estimation, we are not an isolated case. But this does not make the move less frustrating or more understandable!

The good news is about the potential translation of our book Introducing Monte Carlo Methods with R into Japanese, as was recently the case for the book of Phil Spector on Data Manipulation with R. There seems to be a reasonable market for R (and Splus) books in Japan for those translations to take place…

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