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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.

ABC [almost] in the front news

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , , , , on July 7, 2014 by xi'an

cow (with TB?) on one of the ghats, Varanasi, Uttar Pradesh, Jan. 6, 2013My friend and Warwick colleague Gareth Roberts just published a paper in Nature with Ellen Brooks-Pollock and Matt Keeling from the University of Warwick on the modelling of bovine tuberculosis dynamics in Britain and on the impact of control measures. The data comes from the Cattle Tracing System and the VetNet national testing database. The mathematical model is based on a stochastic process and its six parameters are estimated by sequential ABC (SMC-ABC). The summary statistics chosen in the model are the number of infected farms per county per year and the number of reactors (cattle failing a test) per county per year.

“Therefore, we predict that control of local badger populations and hence control of environmental transmission will have a relatively limited effect on all measures of bovine TB incidence.”

This advanced modelling of a comprehensive dataset on TB in Britain quickly got into a high profile as it addresses the highly controversial (not to say plain stupid) culling of badgers (who also carry TB) advocated by the government. The study concludes that “only generic measures such as more national testing, whole herd culling or vaccination that affect all routes of transmission are effective at controlling the spread of bovine TB.” While the elimination of badgers from the English countryside would have a limited effect.  Good news for badgers! And the Badger Trust. Unsurprisingly, the study was immediately rejected by the UK farming minister! Not only does he object to the herd culling solution for economic reasons, but he “cannot accept the paper’s findings”. Maybe he does not like ABC… More seriously, the media oversimplified the findings of the study, “as usual”, with e.g. The Guardian headline of “tuberculosis threat requires mass cull of cattle”.

sunrise over Warwickshire (#2)

Posted in pictures, Running, Travel, University life with tags , , , , , on July 4, 2014 by xi'an

UWpond

sunset over Warwickshire

Posted in pictures, Running, Travel, University life with tags , , , , , on July 3, 2014 by xi'an

Warise

back in Warwick

Posted in pictures, Running, Travel, University life with tags , , , on July 2, 2014 by xi'an

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