## let the evidence speak [book review]

Posted in Books, Kids, Statistics with tags , , , , , , , , , , on December 17, 2018 by xi'an

This book by Alan Jessop, professor at the Durham University Business School,  aims at presenting Bayesian ideas and methods towards decision making “without formula because they are not necessary; the ability to add and multiply is all that is needed.” The trick is in using a Bayes grid, in other words a two by two table. (There are a few formulas that survived the slaughter, see e.g. on p. 91 the formula for the entropy. Contained in the chapter on information that I find definitely unclear.) When leaving the 2×2 world, things become more complicated and the construction of a prior belief as a probability density gets heroic without the availability of maths formulas. The first part of the paper is about Likelihood, albeit not the likelihood function, despite having the general rule that (p.73)

belief is proportional to base rate x likelihood

which is the book‘s version of Bayes’ (base?!) theorem. It then goes on to discuss the less structure nature of prior (or prior beliefs) against likelihood by describing Tony O’Hagan’s way of scaling experts’ beliefs in terms of a Beta distribution. And mentioning Jaynes’ maximum entropy prior without a single formula. What is hard to fathom from the text is how can one derive the likelihood outside surveys. (Using the illustration of 1963 Oswald’s murder by Ruby in the likelihood chapter does not particularly help!) A bit of nitpicking at this stage: the sentence

“The ancient Greeks, and before them the Chinese and the Aztecs…”

is historically incorrect since, while the Chinese empire dates back before the Greek dark ages, the Aztecs only rule Mexico from the 14th century (AD) until the Spaniard invasion. While most of the book sticks with unidimensional parameters, it also discusses more complex structures, for which it relies on Monte Carlo, although the description is rather cryptic (use your spreadsheet!, p.133). The book at this stage turns into a more story-telling mode, by considering for instance the Federalist papers analysis by Mosteller and Wallace. The reader can only follow the process of assessing a document authorship for a single word, as multidimensional cases (for either data or parameters) are out of reach. The same comment applies to the ecology, archeology, and psychology chapters that follow. The intermediary chapter on the “grossly misleading” [Court wording] of the statistical evidence in the Sally Clark prosecution is more accessible in that (again) it relies on a single number. Returning to the ban of Bayes rule in British courts:

In the light of the strong criticism by this court in the 1990s of using Bayes theorem before the jury in cases where there was no reliable statistical evidence, the practice of using a Bayesian approach and likelihood ratios to formulate opinions placed before a jury without that process being disclosed and debated in court is contrary to principles of open justice.

the discussion found in the book is quite moderate and inclusive, in that a Bayesian analysis helps in gathering evidence about a case, but may be misunderstood or misused at the [non-Bayesian] decision level.

In conclusion, Let the Evidence Speak is an interesting introduction to Bayesian thinking, through a simplifying device, the Bayes grid, which seems to come from management, with a large number of examples, if not necessarily all realistic and some side-stories. I doubt this exposure can produce expert practitioners, but it makes for an worthwhile awakening for someone “likely to have read this book because [one] had heard of Bayes but were uncertain what is was” (p.222). With commendable caution and warnings along the way.

## postdoc position in London plus Seattle

Posted in Statistics with tags , , , , , , , , , , , on March 21, 2018 by xi'an

Here is an announcement from Oliver Ratman for a postdoc position at Imperial College London with partners in Seattle, on epidemiology and new Bayesian methods for estimating sources of transmission with phylogenetics. As stressed by Ollie, no pre-requisites in phylogenetics are required, they are really looking for someone with solid foundations in Mathematics/Statistics, especially Bayesian Statistics, and good computing skills (R, github, MCMC, Stan). The search is officially for a Postdoc in Statistics and Pathogen Phylodynamics. Reference number is NS2017189LH. Deadline is April 07, 2018.

## more positions in the UK [postdoc & professor]

Posted in Statistics with tags , , , , , , , , , , , on October 13, 2017 by xi'an

1. The University of Bristol is seeking to appoint a number of Chairs in any areas of Mathematics or Statistical Science, in support of a major strategic expansion of the School of Mathematics. Deadline is December 4.
2. Durham University is opening a newly created position of Professor of Statistics, with research and teaching duties. Deadline is November 6.
3. Oliver Ratman, in the Department of Mathematics at Imperial College London, is seeking a Research Associate in Statistics and Pathogen Phylodynamics. Deadline is October 30.

## When Buffon meets Bertrand

Posted in R, Statistics, Travel with tags , , , , , on April 7, 2011 by xi'an

When Peter Diggle gave his “short history” of spatial statistics this morning (I typed this in the taxi from Charles de Gaulle airport, after waiting one hour for my bag!), he started with a nice slide about Buffon’s needle (and Buffon’s portrait), since Julian Besag was often prone to give this problem as a final exam to Durham students (one of whom is responsible for the candidate’s formula). This started me thinking about how this was open to a Bertrand’s paradox of its own. Indeed, randomness for the needle throw can be represented in many ways:

• needle centre uniformly distributed over the room (or the perpendicular to the boards) with a random orientation (with a provision to have the needle fit);
• needle endpoint uniformly distributed over the room (again a uniform over the perpendicular is enough) with a random orientation (again with a constraint);
• random orientation from one corner of the room and a uniform location of the centre on the resulting line (with constraints on both ends for the needle to fit);
• random orientation from one corner of the room and a uniform location of one endpoint on the resulting line, plus a Bernoulli generation to decide on the orientation (with constraints on both ends for the needle to fit);
• &tc.

I did not have time to implement those different generation mechanisms in R, but have little doubt they should lead to different probabilities of intersection between the needle and one of the board separations. I actually found a web-page at the University of Alabama Huntsville addressing this problem through exercises (plus 20,000 related entries! Including von MisesProbability, Statistics and Truth itself. A book I should read one of those days, following Andrew.). Note that each version corresponds to a physical mechanism. Thus that there is no way to distinguish between them. Had I time, I would also like to consider the limiting case when the room gets infinite as, presumably, some of those proposals would end up being identical.