Archive for Bayes theorem

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.

an easy pun on conditional risk[cd]

Posted in Books, Kids, Statistics with tags , , , , on September 22, 2013 by xi'an

Albert Jacquard (1925-2013)

Posted in Books, Statistics with tags , , , , , , on September 21, 2013 by xi'an

Albert Jacquard passed away last week. He was a humanist, engaged in the defence of outcasts (laissés pour compte) like homeless and illegal immigrants. He had a regular chronicle of two minutes on France Culture that I used to listen to (when driving at that time of the day). In the obituaries published in the recent days, this side of the character was put forward, while very little was said about his scientific legacy. He was a statistician, first at INSEE, then at INED. After getting a PhD in genetics from Stanford in 1968, he got back to INED as a population geneticist, writing in 1978 his most famous book, Éloge de la Différence, against racial theories, which is the first in a long series of vulgarisation and philosophical books. Among his scientific books, he wrote the entry on Probabilités in the popular vulgarisation series “Que Sais-Je?”, with more than 40,000 copies sold and used by generations of students. (Among its 125 pages, the imposed length for a  “Que Sais-Je?”, the book includes Bayes theorem and, more importantly, the Bayesian approach to estimating unknown probabilities!)

the original xkcd entry on Bayes [with its mistake]

Posted in Books, Kids, Statistics with tags , on July 13, 2013 by xi'an

Bayes is back on xkcd

Posted in Books, Kids, Statistics with tags , , , on July 12, 2013 by xi'an

my statistician friend

Posted in Books, Kids, Running, Statistics, University life with tags , , , on April 7, 2013 by xi'an

A video made in Padova:(and shown during a break at the workshop), watch out for Bayes’ theorem!

Bayes on the radio (regrets)

Posted in Books, Kids, Running, Statistics with tags , , , , , on November 13, 2012 by xi'an

While running this morning I was reconsidering (over and over) my discussion of Bayes’ formula on the radio and thought I should have turned the presentation of Bayes’ theorem differently. I spent much too much time on the math side of Bayes’ formula and not enough on the stat side. The math aspect is not of real importance as it is a mere reformulation of conditional probabilities. The stat side is what matters as introducing a (prior) distribution on the parameter (space) is the #1 specificity of Bayesian statistics…. And the focus point of most criticisms, as expressed later by the physicist working on the Higgs boson, Dirk Zerwas.

I also regret not mentioning that Bayes’ formula was taught in French high schools, as illustrated by the anecdote of Bayes at the bac. And not reacting at the question about Bayes in the courtroom with yet another anecdote of Bayes’ formula been thrown out of the accepted tools by an English court of appeal about a year ago. Oh well, another argument for sticking to the written world.

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