Archive for May, 2011

Questions on ABC

Posted in Statistics, University life with tags , , , , , , on May 31, 2011 by xi'an

Our ABC survey for Statistics and Computing (and the ABC special issue!) has been quickly revised, resubmitted, and rearXived. Here is our conclusion about some issues that remain unsolved (much more limited in scope than the program drafted by Halton!):

  1. the convergence results obtained so far are unpractical in that they require either the tolerance to go to zero or the sample size to go to infinity. Obtaining exact error bounds for positive tolerances and finite sample sizes would bring a strong improvement in both the implementation of the method and in the assessment of its worth.
  2. in particular, the choice of the tolerance is so far handled from a very empirical perspective. Recent theoretical assessments show that a balance between Monte Carlo variability and target approximation is necessary, but the right amount of balance must be reached towards a practical implementation.
  3.  even though ABC is often presented as a converging method that approximates Bayesian inference, it can also be perceived as an inference technique per se and hence analysed in its own right. Connections with indirect inference have already been drawn, however the fine asymptotics of ABC would be most useful to derive. Moreover, it could indirectly provide indications about the optimal calibration of the algorithm.
  4. in connection with the above, the connection of ABC-based inference with other approximative methods like variational Bayes inference is so far unexplored. Comparing and interbreeding those different methods should become a research focus as well.
  5. the construction and selection of the summary statistics is so far highly empirical. An automated approach based on the principles of data analysis and approximate sufficiency would be much more attractive and convincing, especially in non-standard and complex settings. \item the debate about ABC-based model choice is so far inconclusive in that we cannot guarantee the validity of the approximation, while considering that a “large enough” collection of summary statistics provides an acceptable level of approximation. Evaluating the discrepancy by exploratory methods like the bootstrap would shed a much more satisfactory light on this issue.
  6.  the method necessarily faces limitations imposed by large datasets or complex models, in that simulating pseudo-data may itself become an impossible task. Dimension-reducing techniques that would simulate directly the summary statistics will soon become necessary.

Reviewer credits

Posted in Statistics, University life with tags , , , on May 30, 2011 by xi'an

Today I completed a referee’s (anonymous) report for Statistical Applications in Genetics and Molecular Biology  and I received the following acknowledgement:

Thank you very much for submitting your review of the manuscript “xxxxxx” for Statistical Applications in Genetics and Molecular Biology. We greatly appreciate your efforts. Should the manuscript be accepted for publication, you will receive a blind copy of the publication notification to the author(s).

Thank you very much also for your promptness. Accordingly, we are pleased to credit your account in the Authors & Reviewers’ Bank with 1 credit(s) for this review. We hope that you will soon use these credits to submit a paper of your own, so that you can take advantage of and enjoy the same prompt attention during the peer review process for your manuscript.

Thank you again for your help. We hope you will send manuscripts to us and continue to referee for us in the near future.

This is a fairly interesting refereeing system where one gains credits (1 or 2) for refereeing papers and burns credits (2 or 3) when submitting papers. In case of a deficit at submission time, one must promise to referee two papers in the near future and leave a credit card deposit against the possibility one later renegade on this promise! The charge is then $200! Rather direct, but fair in the way that one has to referee papers if one expects others to referee one’s papers. (I wonder if there is a black market for selling those credits…!)

Prix Le Monde Jeune Economiste 2011

Posted in Books, University life with tags , , , , on May 29, 2011 by xi'an

Each year, Le Monde nominates a French economist for its Jeune Economiste Prize. The past winners are

(Some of those recipients are or were researchers at CREST. And Elyès is my colleague in Paris-Dauphine. When he is not minister in Tunisia!) The 2011 winner is Xavier Gabaix, who is professor of economics at NUY. I know nothing of his research and of its impact on Economics, nor do I want to to criticise the 2011 prize in any respect, however in a fairly bland and uninformative interview with Le Monde, Xavier Gabaix focused on the Zipf laws (connected with the Benford law I mentioned a while ago about the Iranian elections):

Pour la théorie économique classique, les phénomènes économiques se distribuent selon une courbe de Gauss (en cloche), et la modélisation raisonne généralement à partir de moyennes, d’agrégats. Or, la recherche a montré que, dans des domaines très variés, la distribution des objets, par exemple par rang de taille pour les villes ou par fréquence d’occurrence pour les mots d’un texte, obéit à des lois mathématiques comme les lois de Zipf, du nom du linguiste qui les a mises en évidence. Dans un article de Nature paru en 2003 et écrit avec des physiciens, j’ai montré que la fréquence des baisses boursières atteignant certains seuils (10 %, 20 %, 30 %) obéissait à la même loi mathématique que la fréquence des séismes… L’observation du volume de transactions boursières, de la taille des firmes, des évolutions de la croissance, permet également de déceler de telles lois de distribution.

which google-translates as

In classical economic theory, economic phenomena are distributed according to a Gaussian (bell) distribution, and modeling reasons usually based on averages and aggregates. However, research has shown that in various fields, the distribution of objects, for example in the size ranks of cities or in the frequency of occurrence of words in a text, obeys mathematical laws such as the Zipf laws, named after the linguist who has identified them. In a Nature paper published in 2003 and written with physicists, I showed that the frequency of stock market declines reaching certain thresholds (10%, 20%, 30%) obey the same mathematical law as the frequency of earthquakes .. . The observation of the volume of stock transactions, the size of firms, changes in growth, can also identify such distributions.

This somehow reminds me of the criticisms on the normal/Gaussian distribution in Nassim Taleb’s (outrageous) Black Swan. I would think the same type of criticism applies here: The interview mentions the fact that a few actors have a considerable impact on financial markets. This kind of observation applies to  an extreme value phenomenon. hence a particularly-difficult-to-estimate statistical problem. Especially given the lack of stationarity on those financial markets…

The Wrecker

Posted in Books, Travel with tags , , , , on May 28, 2011 by xi'an

“Full of details of our barbaric manners and unstable morals; full of the need and the lust of money, so that there is scarce a page in which the dollars do not jingle; full of the unrest and movement of our century, so that the reader is hurried from place to place and sea to sea, and the book is less a romance than a panorama.” R.L. Stevenson

Despite a strong appreciation for other books of his’, I was not aware of Robert L. Stevenson’s The Wrecker until Judith Rousseau lent it to me a few months ago. It took me a while to start the novel, maybe because of its kind of kaleidoscopic style with tales within tales within tales…, but past a certain point, I became engrossed in the reading and could not stop till I completed The Wrecker! (Note that the book is freely available for Kindle on amazon!)

“I can never think upon this voyage without a profound sense of pity and mystery; of the ship (once the whim of a rich blackguard) faring with her battered fineries and upon her homely errand, across the plains of ocean, and past the gorgeous scenery of dawn and sunset; and the ship’s company, so strangely assembled…” R.L. Stevenson

The Wrecker is a great travel book, most of the action taking place in the South Pacific seas, with connections in San Francisco, Edinburgh, and even Barbizon. While the main character (and the main point of view) is Dodd Loudon (a Glaswegian name), there are several tales inserted inside his story, especially the resolution of the mystery of the Flying Scud, the boat for which Loudon and his associate Pinkerton go bankrupt, all for nothing. While I enjoy very much the description of the attraction of the southern seas on Dodd, the last two-thirds of The Wrecker on the search for the Flying Scud and then the pursuit of Carthew, the only remaining member of the Flying Scud, are reminding me of Stevenson’s other books, particularly the Scottish ones like Kidnapped (also free!) and Catriona (again free for Kindles), for the exceptionally gripping pace he can impose on the reader. While the book abounds in 19th century style descriptions, they amazingly do not cut this pace but on the opposite contribute to make it more real. I am thus little surprised that Borges loved this book as it is a literary masterpiece, but also because it contributes to the ambiguity between reality and fantasy, and to the endless spiral of alternative realities that Borges liked so much.

Hammersley and Handscomb 1964 on line

Posted in Books, R, Statistics with tags , , , , on May 27, 2011 by xi'an

Through the webpage of the Advanced Monte Carlo Methods I & II, given a few years ago by Michael Mascagni at ETH Zürich, I found a link to the scanned version of the 1964 book Monte Carlo Methods by Hammersley and Handscomb. This is a short book, with less than 150 pages, especially if one skips the physics applications, and I will certainly take a look at it in the coming days, following the reading of Halton’s 1970 survey.

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