International Society for Bayesian Analysis

As usual, reading the latest issue of Significance is quite pleasant and rewarding (although as usual I have to compete with my wife to get hold of the magazine!). This current issue is dedicated to the (London) Olympics. With articles on predictions of future records, on whether or not the 1988 records can be beaten (the Seoul Olympics were the last games before more severe anti-drug tests were introduced), on advices to Usain Bolt for running faster (!) and on the objective dangers of dying from running a marathon (answer: it is much more “dangerous” to train!).

However, a most puzzling (and least statistical) article is Stephanie Kovalchik’s proposal for a gender-neutral Olympics.  The author’s theme is that, in most sports (the exceptions being shooting, yachting, and horse riding, where competitions are mixed), raw performances of women are below those of men for physical and physiological reasons. Stephanie Kovalchik thus “question[s] whether a sex-stratified Olympics is the product of groundless stereotypes about male athletic superiority or could be justified by gender differences at the elite level of sport” (p.20). Unsurprisingly, she concludes that no amount of training seems capable to bring both sexes at the same level: indeed, for instance, Paula Radcliffe, the fastest female marathon runner (2:15:24), is still 11 minutes beyond Patrick Makau, the fastest male marathon runner (2:03:38). They are both super-terrific athletes, the top ones in their categories. Now, Paula runs half-marathon and marathon faster than the best male runners in my team (Insee Paris Club). Where’s the problem?! And why should we try to rank Paula against Patrick?!

A parenthesis: the author mentions a most bizarre (but eventually inappropriate) exception: in the Badwater Ultramarathon, a crazy race covering 135 miles and going from Badwater, Death Valley, at 280’ (85m) below sea level, to the Mt. Whitney Portals at nearly 8,300’ (2530m), with a total of 13,000’ (3962m) of cumulative vertical ascent, four women won over the 25 occurrences of the race. I found this phenomenon quite curious and went to check first the records of the comparable ultra-trail du Mont Blanc, another even crazier race (168km, 9,600 metres of positive height gain, at mostly higher altitudes, between 1000m and 2500m), and saw that last year the first woman in the race was 13th in total, with a difference of four and a half hours with the winner (20:36 hours, believe it or not..!). Going back to the Badwater Ultramarathon, checking the results showed that the race actually attracts a very limited number of runners, from 17 finishers the first year to 83 last year (where the first woman was 7th, about 5 hours from the winner), with a huge variation between runners and between years. So I would not draw so much of a conclusion from this example, certainly not that “in an event where sheer dogged endurance, guts and determination must count for almost everything, we may be there already”. It is rather a law of small numbers: such extreme events attract a very small number of participants with incredibly variable finishing times, e.g. two of the four winning women won out of…5 (1988) and 2 (1989) finishers, while the two other victories were achieved by Pamela Reed over 45 (2003) and 57 (2002) competitors, a much more remarkable feat. Meaning that one or two runners missing or giving up brings a huge change in the final time. The ultra-trail du Mont Blanc now involves a thousand runners and there, numbers count. End of the parenthesis (with total respect to all those runners, I wish I could do it!).

Going back to the paper proposal, Stephanie Kovalchik considers that “credit merit apart from hereditary luck will favour individuals who possess the best genes for sport. Thus, prejudice – in the true sense of pre-judging – at the Olympics runs deeper than gender lines. Geneticism more than sexism is to blame for making the possession of a Y chromosome an advantage at the Games” (p.21). She suggests to instead rank athletes by a “statistical adjustment [that would]  remove the confounding factor of genetic inheritance, to provide a standard of achievement that all could aim at, no matter what their hereditary luck” (p.22). In essence, the winner would be the one that had gained the most compared with a “demographically matched sample of untrained individuals” (p.24). If I may, this sounds perfectly ridiculous! First, the whole point of the Games and of any sporting competition is to determine the “best” athlete. This is not an egalitarian goal and can and does lead to poor outcomes such as cheating, drug enhanced performances, nationalistic recuperations, commercialisation, bribery, and so on. It is thus perfectly coherent to be against those competitions. (I am not a big fan of the Olympics myself for this reason. However, without competition, even at my very humble level, and with little hope of winning anything, I would certainly train much less than I currently do.) But to try to reward efforts to counteract physical differences sounds like political correctness pushed to the extreme!  Second, and this is why I find the paper so a-statistical!, the adjustment must be with respect to a reference population. If we carry the argument to its limit, the only relevant population is made of the athlete him/herself. Indeed, genetic, sociological, cultural, geographical, financial, you-name-it, elements should all be taken into account! Which obviously makes the computation just impossible because then everyone is competing against him/herself.

A recent arXiv posting of the paper “On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling” by Martino, Luengo, and Míguez from Madrid rekindled my interest in this rather peculiar simulation method. The ratio of uniforms samples uniformly on the subgraph

to produce simulations from p as the ratio v/u. The proof is straightforward first year calculus but I do not find the method intuitive as, say, accept/reject…. The paper gives a very detailed background on those methods, as well as on the “inverse of density method”, which is like looking at the uniform simulation over the subgraph, but with both axes inverted (slice sampling is the same on both). (A minor point of contention or at least misunderstanding: when using the inverse of density method, the authors claim that using the unormalised and the normalised versions of the target leads to the same outcome. While it is true for the direct method, I have trouble seeing the equivalent in the inverse case…) The paper also stresses that the optimal case for accept-reject is when the target is bounded because the uniform can then be used as a proposal. I agree this is a simpler solution but fail to see any optimality in the matter. The authors then study ways of transforming unbounded subgraphs into bounded domains (i.e. bounded pdfs and supports). This imposes conditions on the transform f, which must have finite limits for p(x)/f’(x) or p-1(x)/f’(x) at the boundaries. (An optimal choice is when f is the cdf of p, since then the transform is uniform.)

The remainder (and more innovative) part of the paper is less clear in that I do not get a generic feeling on what it is about! The generalisation of the above is to consider uniform sampling from

for a generic increasing function g such that g(0)=0. And c a positive constant. (Any positive constant?!) But this is from a 1991 paper by Jon Wakefield, Alan Gelfand, and Adrian Smith. The extension is thus in finding g such that the above region is bounded and can be explored by uniform sampling over a box.. And in noticing that “the generalized Ratio-of-Uniform method is a combination of the transformed rejection method applied to the inverse density with the extended inverse-of-density method” (p.27).

I wonder at the applicability of the approach for costly target functions p. And at the extension to larger dimensions. And wish I had more time (or more graduate students) to look at possible adaptive constructions of the transform g. An interesting and fruitful read, nonetheless!

Today, I will spend my day in thesis defenses, as I take part in a defense committee this morning at Supéléc, about a thesis written by Alireza Roodaki on a new approach to trans-dimensional MCMC for mixtures of distributions. Rather than a new way to simulate from posterior distributions with a varying number of components, the thesis concentrates on the post-simulation processing of the outcome of the simulation, constructing an object similar to the point process representation of Matthew Stephens where components have a meaning across varying dimensions. An interesting and novel perspective. The afternoon, I am part of another defense committee for the habilitation of Fadoua Balabdaoui, my colleague in Paris-Dauphine. Fadoua is working in non-parametric statistics, under shape constraints, but has a wide range of interests and publications that fully justify an habilitation degree at this stage of her career. (Habilitation is a degree required in France and Germany to become a Full Professor and to autonomously advise PhD students.)

I bought this book in Princeton bookstore mostly because it was a such beautiful object! I had never heard of Nathan Larson nor of the Dewey Decimal System when I grabbed the book and felt the compulsion to buy it!

The book published by Akashic Books is indeed a beautiful book: the paper is high quality, a warm crème colour, the cover has inside flaps, the printing makes reading very enjoyable, the pages are cut in such a way that looking at the book from the fore edge makes it look like a Manhattan skyline… Truly a beautiful thing!!!

Once I had opened the book, I also got trapped by the story, an unusual style along with a great post-apocalyptic plot (not The Road, of course!, but what can compare with The Road?!) and a love of New York City that permeates the pages for sure! A magistral début for a new author. While the action takes place in an unpleasant future New York City, with disease and ruin on ever street corner, slowly recovering from a mega 9/11 style attack, the central character relates very much to Chandler‘s private detectives, but also, as mentioned in another review, to Jerome Charyn’s Isaac Seidel! The main character, only known as Dewey Decimal for his maniac idée fixe of ordering the books in the New York Library where he lives, is bordering on the insane and his moral code is rather heavily warped, witness several rather gratuitous murders in the book,  but the whole city seems to have fallen very low in terms of this same moral code… As well as being under the rule of Eastern European thugs (to the point of the hero speaking Russian and Ukrainian). The blonde fatale found in every roman noir is slightly carituresque (“plastic surgery in any amount just makes me want to puke. Call me judgmental, but it indicates a certain set of accompanying goals, fashion choices and behaviors. It’s trashy and it means you don’t like yourself.“), with whiffs of ethnic cleansing activities in Serbia and she remains a mystery till the end of the novel. As are most other characters, in fact. This may be the low tide part of the book, that everything is perceived from Dewey’s eyes to the point of making others one-D and hard to fathom… But the overall scheme of following this partly insane detective throughout New York City makes the Dewey Decimal System quite an unconventional pleasure to read and I am looking forward the next story in the series.

Being freshly elected ASA Fellow (yay!), I just received the list of 2012 ASA Fellows. Among whose, let me mention

• Sudipto Banerjee, University of Minnesota, Minneapolis, Minnesota, elected “For theoretical, methodological and applied research in spatiotemporal statistical modeling, especially as applied to problems in environmetrics, ecology, occupational health, agriculture and economics, for professional work at the local and national levels and for editorial service to the profession.”
• Thomas Lumley, University of Auckland, Auckland, New Zealand, elected “For outstanding contributions to statistical theory and practice; for influential collaborations benefiting many important scientific studies; and for implementation of new methodology through the R system and the development of specialist software packages.”
• Bhramar Mukherjee, University of Michigan, Department of Biostatistics, Ann Arbor, Michigan, elected “For influential research on Bayesian methods for analysis of gene-environment interactions and data generated under case-control and outcome dependent sampling mechanisms, for insightful consulting and collaboration with genetic scientists, for superb teaching and mentoring of both majors and non-majors of biostatistics, and for steadfast service to the profession.”
• Marc A. Suchard, UCLA, Los Angeles, California, elected “For his wide-ranging, insightful and influential contributions to computational statistics, stochastic processes, Bayesian modeling and computing, evolutionary medicine, bioinformatics, and computational biology; for innovative models and contributions to the analysis of phylogeny, alignment, gene transfer and phylogeography.”
• Thaddeus Tarpey, Wright State University, Dayton, Ohio, elected “For influential contributions to statistical research and applications, particularly in the areas of multivariate analysis and for excellence in teaching and dissemination of statistical knowledge.”

The cover for the final volume of Robert Jordan’s and Brandon Sanderson‘s the Wheel of Time,  A Memory of Light, has just appeared. Although the artist has changed, from Darrell K. Sweet who passed away before completing his cover to Michael Whelan, I find the cover as appalling as the previous thirteen covers in the series… With the same frozen features and caricaturesque characters, unrealistic depictions (look at the way Rand holds this sword!) and women at the back. I know, I know, I should not expect highly creative covers for fantasy books, but other recent books have managed much better, from Sanderson’s Mistborns (other series of Sanderson do not succeed so well, incl. Elantris) to Abercrombie’s trilogy (and his The Heroes), admittedly the coolest covers so far, to Morgan’s The Steel Remains, to Karen Miller’s series of The prodigal mage … Even the alternative e-book covers for  the Wheel of Time are quite acceptable, so I really wonder why the publisher sticks at those ugly and outdated covers.  Anyway, this is now a sort of tradition! The final volume is planned for early January 2013, which is in tune with what Brandon Sanderson told us last year when giving a public lecture in Paris. There is much expectation about this book, the culmination of a series I started reading more than 20 years ago!

Elsevier is launching a new journal called Spatial Statistics, whose goal is…

“…to be the leading journal in the field of spatial statistics. It publishes articles at the highest scientific level concerning important and timely developments in the theory and applications of spatial and spatio-temporal statistics. It favors manuscripts that present theory generated by new applications, or where new theory is applied to an important spatial problem.”

Given the Elsevier tradition of charging absurd amounts for journals, this journal is “only” 475 euros / USD 662 for libraries and institutions. (Which is actually a lot for a new journal with no credential. And does not mean much given the “bundling” strategy of Elsevier.) And there are caveats, like the unbelievable fee of $3,000 for Open Source publishing (“excludes taxes and other potential author fees”…) and the prohibition to post the final version of one’s paper on arXiv. (what the journal turns into a beautifully newspeak “right”: “the right to post a pre-print version of the journal article on Internet websites“). Hence, as much as I appreciate the idea of dedicating a journal to the many issues pertaining to the specific area of spatial statistics, I stick with my support of The Cost of Knowledge pledge “not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal“. (Elsevier has recently responded to this boycott call by making minor proposals analysed in depth by Tim Gowers.)

Here is the announcement for the second “Journée Darwin“, which will take place on Friday, May the 11th [keep their tusks!], in Chimie ParisTech (near Institut Henri Poincaré),  Amphithéâtre Friedel, starting at 9h30:

The “Journées Darwin” are a series of meetings aimed at bringing together researchers in the Parisian basin working on biological evolution. Each “Journée” consists in a small number of seminars, in which the speakers are expected to explain the philosophy and the perspectives motivating their research, focusing on long-range goals rather than on immediate results. The goal is to help in establishing connections among researchers interested in different aspects of biological evolution, working on different systems and in different laboratories.

Kerrie Mengersen (QUT, Brisbane, visiting Paris-Dauphine and CREST) is giving a talk tomorrow at 4:30pm at Institut Henri Poincaré, during the Séminaire Big’MC, following a talk by Meili Baragatti (MISTEA, SupAgro) on parallel tempering ABC (I discussed in this post):

Understanding images: from inferential aims to models to algorithms

In the excitement of working with algorithms, it is sometimes salutary to remind ourselves of their purpose. In this presentation, we consider the analysis of image data and try to match inferential aims, models and computational methods. We describe and compare the approaches in the context of some real case studies in agriculture and environmental monitoring.

Answering a question around this theme on StackExchange, I wrote the following reply:

The debate about non-informative priors has been going on for ages, at least since the end of the 19th century with criticisms by Bertrand and de Morgan about the lack of invariance of Laplace’s uniform priors (the same criticism reported by Stéphane Laurent in the above comments). This lack of invariance sounded like a death stroke for the Bayesian approach and, while some Bayesians were desperately trying to cling to specific distributions, using less-than-formal arguments, others had a wider vision of a larger picture where priors could be used in situations where there was hardly any prior information, beyond the shape of the likelihood itself. (This was even before Abraham Wald established his admissibility and complete class results about Bayes procedures. And at about the same time as E.J.G. Pitman gave an “objective” derivation of the best invariant estimator as a Bayes estimator against the corresponding Haar measure…)

This vision is best represented by Jeffreys’ distributions, where the information matrix of the sampling model, , is turned into a prior distribution

which is most often improper, i.e. does not integrate to a finite value. The label “non-informative” associated with Jeffreys’ priors is rather unfortunate, as they represent an input from the statistician, hence are informative about something! Similarly, “objective” has an authoritative weight I dislike… I thus prefer the label “reference prior”, used for instance by José Bernado.

Those priors indeed give a reference against which one can compute either the reference estimator/test/prediction or one’s own estimator/test/prediction using a different prior motivated by subjective and objective items of information. To answer directly the question, “why not use only informative priors?”, there is actually no answer. A prior distribution is a choice made by the statistician, neither a state of Nature nor a hidden variable. In other words, there is no “best prior” that one “should use”. Because this is the nature of statistical inference that there is no “best answer”.

Hence my defence of the noninformative/reference choice! It is providing the same range of inferential tools as other priors, but gives answers that are only inspired by the shape of the likelihood function, rather than induced by some opinion about the range of the unknown parameters.

We have now completed our revision of the paper Relevant statistics for Bayesian model choice, written with Judith Rousseau, Jean-Michel Marin, and Natesh Pillai. It has been resubmitted to Series B and reposted on arXiv. The major change in the paper is the inclusion of a check about the relevance of a given summary statistics, as already explained in the talks I presented in Bristol and Glasgow. We also ran a realistic (and, I think, illuminating!) experiment to assess the impact of using one or two (δμ)² statistics as summaries in a simple population experiment, along with a theoretical explanation of the difference between both cases. This methodological addition answers in my opinion the major criticism contained in the review and I thus hope we can envision the eventual publication of this paper… In any case, the reviews have been tremendously helpful in improving the paper.

Iain Murray and Lloyd T. Elliott had posted this paper on arXiv just before I left for my U,K, 2012 tour and I did not have time to read it in detail, nor obviously to report on it. Fortunately, during the ICMS meeting, Iain presented an handmade poster on this paper that allowed me a quick tour, enough to report on the contents! The main point of the paper is that it is possible to modify many standard MCMC codes so that they can be driven by a dependent random sequence. The authors show that various if specific dependent sequences of uniform variates do not modify the right target and the ergodicity of the MCMC scheme. As mentioned in the conclusion of the paper, this may have interesting consequences in parallel implementations where randomness becomes questionable, or in physical random generators, whose independence may also be questionable…

Following Flags of our Fathers a few weeks ago, I watched Clint Eastwood’s Letters from Iwo Jima last weekend. I had wanted to see those movies for quite a while (!) but never found the time till now.. While being a long time fan of Clint Eastwood (the director), I was rather disappointed with Flags of our Fathers, because part of the movie takes place in America after the battle. The intensity of the Iwo Jima battle and the many lost lives occurring therein does not level with the side story of the flag and of the soldiers substitution and of their tour of America. While I presume this opposition is voluntary and aims at exposing the absurdity of this état de fait, as well as the transformation of those soldiers into icons, mostly against their will, it is somehow too intellectual and remote to relate to. I also felt the three soldiers chosen for the task were too caricaturesque. Again, this presumably reflects the choice made by the authorities to boost the war bonds, but it does not help in making the movie emotionally intense, something to share in, as a more linear story-line (as in Saving Private Ryan) would have…

The second movie of the diptych, Letters from Iwo Jima, is much more powerful for this reason: a small group of soldiers is followed throughout the battle, with few flashbacks and no flashforwards. The battle scenes are rather subdued, compared with the very strong battle actions of Flags of our Fathers, and the successive deaths of all characters are more like removals than battle kills, in a subterranean huis-clos… (Actually, there is much less mirror plays between both movies than I would have thought: there is no scene paralleled from one movie to the next, except for the landing of the American troops.) It is a common feature of both movies that  the enemy is rarely visible, hardly ever identified as a human being. In Letters from Iwo Jima, there is only one American soldier that comes into contact with the Japanese soldiers, when injured. (I do not remember if any live Japanese soldier is visible throughout the other movie.) The fact that the dialogues are in Japanese makes the story more genuine, which is a good scenario trick, as it blurs any unrealistic or caricaturesque feature… In retrospect, the characters also are caricaturesque, from the baker who is drafted to war against his will to the fanatic and idiotic nationalists, to the charismatic, intellectual, and intelligent commandeer in chief who sees beyond the propaganda but nonetheless sticks to his duty.  Still, despite or because of those scenari tricks, I deeply appreciated this movie.

I spent most of the Sunday afternoon trying to understand why defining

\newcommand{\era}{\end{comment}}

did not have the same effect as writing the line

\end{comment}

until I found there is a clash due to the comment package… The assuredly simple code

\documentclass{book} \usepackage{comment} \begin{document} \begin{comment} prompt, you could embark on an on-line visit of the main features of {\tt R} by typing \verb+demo()+ after the prompt (make sure to test \verb+demo(image)+ and \verb+demo(graphics)+ to get an idea of the \era Self-explanatory. \end{document}

produces an error message:

Runaway argument? ! File ended while scanning use of \next. <inserted text> \par <*> moretest.tex

This is quite an inconvenience as I need to compile my solution manual for “Introducing Monte Carlo Methods with R” with the even-numbered exercises commented out or not depending on the version… (Leaving this package out and using the comment command within the verbatim package does not work either because era does not seem to be recognised as the end of a commented part…)

Nicolas Chopin sent me this piece after reading Larry’s radical proposal. And my post on it. This is a preliminary version, so feel free to comment!

In a provocative column in the latest ISBA Bulletin, Larry Wasserman calls for “a world without referees”. This is an interesting read, not devoid of mala fide arguments (“We are using a refereeing system that is almost 350 years old. If we used the same printing methods as we did in 1665 it would be considered laughable.”), but this is hard to avoid, given how passionate this subjects is for many scientists. In this article, I’d like to propose a defense of the too often derided referee, arguing that a system that has served us so well for 350 years cannot be ditched so easily.

To start with, talking about getting rid of peer-reviewing is a bit of idle talk, as we all know it is never going to happen. In fact, it’s a perfect example of the prisoner’s dilemma. Stopping to send papers to journals would make sense only if a majority of scientists would decide to do so simultaneously. But, for many of us, so much depends on our publication record (including jobs, promotions, grants, even salaries in certain institutions) that very few would dare to “shoot first”. And, even if we assume a given field would be ready to do so (say all the statisticians), would that such a move make any sense, without all the other fields of Science doing it also at the same time? The prisoner’s dilemma simply moves to a higher level, as scientific fields are also competing for grants, jobs openings and so on.

I think US scientists would be surprised to see how regular, yet basic and dumbly quantitative is the evaluation of research by governments and Universities in most countries. This is certainly unfortunate, but it reinforces the prisoner’s dilemma I am talking about.

The previous section seems to make the usual argument that refereeing is a necessary evil. We believe on the contrary it is a necessary good. Yes, certain referees are annoying, or even aggressive or too dismissive about our work. Of course, like Larry, we can tell several horror stories about referees completely missing the point, or even perhaps being outright dishonest.

But, ego bruising and venting aside, all this is beside the point. The real question is: does refereeing increase the quality of our papers? or is it just “noise”, as stated by Larry?

My personal experience is that all my papers have benefited from refereeing. The most extreme example I can share is that of a very obnoxious referee which was obviously doing all his best to get my paper rejected (while making me add irrelevant references, probably his), and managed to point out a mistake in my rejection algorithm during the third revision. How glad I am to have had such a nitpicking referee in this case. Publishing a wrong paper is much more damaging in the long run than getting rejected. Plus, getting rejected is not such a big deal. If the paper is worth it, we always find the energy to submit it elsewhere, hopefully in a better shape.

In fact, the only referee I fear is the sloppy one who quickly reads the paper and thinks he “gets it”. But usually associate editors are good at spotting these, so this does occur so often.

I also believe that our papers get improved “preemptively” by refereeing; that is, we write better papers because we know it is going to be evaluated by colleagues. We go the extra mile, chase typos, think more carefully about real examples, and so on. And, finally, refereeing simply filters the very long tail of bad papers. How glad I am that referees guard the gates of my favorite journals against them. Please do not ask me instead to check every other paper on arXiv. I don’t have the time, when I do it, I’m strongly biased in favor of authors I know well (like Larry), so this is not fair, and it does not make sense in the first place that all of us replicate this filtering. Plus, from the papers I review, I can see that quite a small proportion of submitted papers are actually send first to arXiv; if all papers were sent there, we would be even less able to deal with this deluge of papers.

Finally, some people seem to be outraged that referees ask certain modifications, because they consider that, as “authors”, they should have an inalienable right to decide the exact form of their texts. But we are not artists (who actually rarely obtain this right anyway), we are scientists, and science (in particular hard science, especially mathematics) works better through consensus on the validity and correctness of the proposed research.

As a final note, Larry’s letter seems to be part of a wider movement of rethinking the way we are dealing with scientific publishing, especially in lights of the “disruptive” impact of the Internet, whatever that oft-used word means. Such questioning is of course welcome. But, as most things, our mental energy comes in limited supply, and should be targeted first at the most glaringly obvious drawbacks of the current system. I am talking of course of the issue of unethical publishers, which is a polite word for thugs. The problem is well-known: we, the scientists, write the papers, evaluate the papers, do the editorial work, everything for free, yet these publishers take our work from us, and charge ridiculous, and ever-increasing, prices for accessing it. Harvard, of all places, cannot afford anymore to pays for journal subscriptions (3.5 millions a year, see an official memorandum). Can you imagine how is the situation in less endowed Universities? This is not sustainable, and we should do our best to get rid of these thugs. This is another subject, but may we quickly urge our readers to sign the current boycott of Elsevier, and prefer to submit to open access journals, such as our beloved Bayesian Analysis‘. Let us push together to get rid of this non-sense.

When this is done, we may return to questioning the refereeing system, and perhaps try to improve on it. One thing I’d like to experiment with would be to reveal the names of referees, not only to the authors, but also to the public, by mentioning their on each publication. That way, referees cannot be either too complacent, or too negative. And at the same time, this would be good recognition of the role of referees, in their help of publishing better research. I would go as far as saying that this would help us to recognize them as co-authors. Not so bad for the poor referee we have been venting at for the last 350 years.

First, apologies for this teaser of a title! This post is not about who is #1 in whatever category you can think of, from statisticians to climbs [the Eiger Nordwand, to be sure!], to runners (Gebrselassie?), to books… (My daughter simply said “c’est moi!” when she saw the cover of this book on my desk.) So this is in fact a book review of…a book with this catching title I received a month or so ago!

“We decided to forgo purely statistical methodology, which is probably a disappointment to the hardcore statisticians.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 225)

This book may be one of the most boring ones I have had to review so far! The reason for this disgruntled introduction to “Who’s #1? The Science of Rating and Ranking” by Langville and Meyer is that it has very little if any to do with statistics and modelling. (And also that it is mostly about American football, a sport I am not even remotely interested in.) The purpose of the book is to present ways of building rating and ranking within a population, based on pairwise numerical connections between some members of this population. The methods abound, at least eight are covered by the book, but they all suffer from the same drawback that they are connected to no grand truth, to no parameter from an underlying probabilistic model, to no loss function that would measure the impact of a “wrong” rating. (The closer it comes to this is when discussing spread betting in Chapter 9.) It is thus a collection of transformation rules, from matrices to ratings. I find this the more disappointing in that there exists a branch of statistics called ranking and selection that specializes in this kind of problems and that statistics in sports is a quite active branch of our profession, witness the numerous books by Jim Albert. (Not to mention Efron’s analysis of baseball data in the 70′s.)

“First suppose that in some absolutely perfect universe there is a perfect rating vector.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 117)

The style of the book is disconcerting at first, and then some, as it sounds written partly from Internet excerpts (at least for most of the pictures) and partly from local student dissertations… The mathematical level is highly varying, in that the authors take the pain to define what a matrix is (page 33), only to jump to Perron-Frobenius theorem a few pages later (page 36). It also mentions Laplace’s succession rule (only justified as a shrinkage towards the center, i.e. away from 0 and 1), the Sinkhorn-Knopp theorem, the traveling salesman problem, Arrow and Condorcet, relaxation and evolutionary optimization, and even Kendall’s and Spearman’s rank tests (Chapter 16), even though no statistical model is involved. (Nothing as terrible as the completely inappropriate use of Spearman’s rho coefficient in one of Belfiglio’s studies…)

“Since it is hard to say which ranking is better, our point here is simply that different methods can produce vastly different rankings.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 78)

I also find irritating the association of “science” with “rating”, because the techniques presented in this book are simply tricks to turn pairwise comparison into a general ordering of a population, nothing to do with uncovering ruling principles explaining the difference between the individuals. Since there is no validation for one ordering against another, we can see no rationality in proposing any of those, except to set a convention. The fascination of the authors for the Markov chain approach to the ranking problem is difficult to fathom as the underlying structure is not dynamical (there is not evolving ranking along games in this book) and the Markov transition matrix is just constructed to derive a stationary distribution, inducing a particular “Markov” ranking.

“The Elo rating system is the epitome of simple elegance.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 64)

An interesting input of the book is its description of the Elo ranking system used in chess, of which I did not know anything apart from its existence. Once again, there is a high degree of arbitrariness in the construction of the ranking, whose sole goal is to provide a convention upon which most people agree. A convention, mind, not a representation of truth! (This chapter contains a section on the Social Network movie, where a character writes a logistic transform on a window, missing the exponent. This should remind Andrew of someone he often refer to in his blog!)

“Perhaps the largest lesson is not to put an undue amount of faith in anyone’s rating.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 125)

In conclusion, I see little point in suggesting reading this book, unless one is interested in matrix optimization problems and/or illustrations in American football… Or unless one wishes to write a statistics book on the topic!