**A**s the Le Monde mathematical puzzle of this week was a geometric one *(the quadrangle ABCD is divided into two parts with the same area, &tc…)* , with no clear R resolution, I chose to bypass it. In this April 3 issue, several items of interest: first, a report by Etienne Ghys on Yakov Sinaï’s Abel Prize for his work “between determinism and randomness”, centred on ergodic theory for dynamic systems, which sounded like the ultimate paradox the first time I heard my former colleague Denis Bosq give a talk about it in Paris 6. Then a frightening fact: the summer conditions have been so unusually harsh in Antarctica (or at least near the Dumont d’Urville French austral station) that none of the 15,000 Adélie penguin couples studied there managed to keep their chick alive. This was due to an ice shelf that did not melt at all over the summer, forcing the penguins to walk an extra 40k to reach the sea… Another entry on the legal obligation for all French universities to offer a second chance exam, no matter how students are evaluated in the first round. (Too bad, I always find writing a second round exam a nuisance.)

## Archive for the R Category

## Le Monde sans puzzle [& sans penguins]

Posted in Books, Kids, R, University life with tags intToBits(), Le Monde, mathematical puzzle, R, StackExchange, stackoverflow on April 12, 2014 by xi'an## data scientist position

Posted in R, Statistics, University life with tags ABC, advanced Monte Carlo methods, École Polytechnique, CREST, Economie et gestion des nouveles données, ENSAE, job offer, machine learning, Matlab, Python, Université Paris Dauphine on April 8, 2014 by xi'an**O**ur newly created Chaire “Economie et gestion des nouvelles données” in Paris-Dauphine, ENS Ulm, École Polytechnique and ENSAE is recruiting a data scientist starting as early as May 1, the call remaining open till the position is filled. The location is in one of the above labs in Paris, the duration for at least one year, salary is varying, based on the applicant’s profile, and the contacts are Stephane Gaiffas (stephane.gaiffas AT cmap DOT polytechnique.fr), Robin Ryder (ryder AT ceremade DOT dauphine.fr). and Gabriel Peyré (peyre AT ceremade DOT dauphine.fr). Here are more details:

**Job description**

The chaire “Economie et gestion des nouvelles données” is recruiting a talented young engineer specialized in large scale computing and data processing. The targeted applications include machine learning, imaging sciences and finance. This is a unique opportunity to join a newly created research group between the best Parisian labs in applied mathematics and computer science (ParisDauphine, ENS Ulm, Ecole Polytechnique and ENSAE) working hand in hand with major industrial companies (Havas, BNP Paribas, Warner Bros.). The proposed position consists in helping researchers of the group to develop and implement large scale data processing methods, and applying these methods on real life problems in collaboration with the industrial partners.

A non exhaustive list of methods that are currently investigated by researchers of the group, and that will play a key role in the computational framework developed by the recruited engineer, includes :

● Large scale non smooth optimization methods (proximal schemes, interior points, optimization on manifolds).

● Machine learning problems (kernelized methods, Lasso, collaborative filtering, deep learning, learning for graphs, learning for timedependent systems), with a particular focus on large scale problems and stochastic methods.

● Imaging problems (compressed sensing, superresolution).

● Approximate Bayesian Computation (ABC) methods.

● Particle and Sequential Monte Carlo methods

Candidate profileThe candidate should have a very good background in computer science with various programming environments (e.g. Matlab, Python, C++) and knowledge of high performance computing methods (e.g. GPU, parallelization, cloud computing). He/she should adhere to the open source philosophy and possibly be able to interact with the relevant communities (e.g. scikitlearn initiative). Typical curriculum includes engineering school or Master studies in computer science / applied maths / physics, and possibly a PhD (not required).

Working environmentThe recruited engineer will work within one of the labs of the chaire. He will benefit from a very stimulating working environment and all required computing resources. He will work in close interaction with the 4 research labs of the chaire, and will also have regular meetings with the industrial partners. More information about the chaire can be found online at http://www.di.ens.fr/~aspremon/chaire/

## Le Monde puzzle [#860]

Posted in Books, Kids, R with tags awalé, Le Monde, mathematical puzzle, R, recursive function on April 4, 2014 by xi'an**A** Le Monde mathematical puzzle that connects to my awalé post of last year:

For N≤18, N balls are placed in N consecutive holes. Two players, Alice and Bob, consecutively take two balls at a time provided those balls are in contiguous holes. The loser is left with orphaned balls. What is the values of N such that Bob can win, no matter what is Alice’s strategy?

**I** solved this puzzle by the following R code that works recursively on N by eliminating all possible adjacent pairs of balls and checking whether or not there is a winning strategy for the other player.

topA=function(awale){ # return 1 if current player can win, 0 otherwise best=0 if (max(awale[-1]*awale[-N])==1){ #there are adjacent balls remaining for (i in (1:(N-1))[awale[1:(N-1)]==1]){ if (awale[i+1]==1){ bwale=awale bwale[c(i,i+1)]=0 best=max(best,1-topA(bwale)) } }} return(best) } for (N in 2:18) print(topA(rep(1,N)))

which returns the solution

[1] 1 [1] 1 [1] 1 [1] 0 [1] 1 [1] 1 [1] 1 [1] 0 [1] 1 [1] 1 [1] 1 [1] 1 [1] 1 [1] 0 [1] 1 [1] 1 [1] 1 <pre>

(brute-force) answering the question that N=5,9,15 are the values where Alice has no winning strategy if Bob plays in an optimal manner**.** (The case N=5 is obvious as there always remains two adjacent 1′s once Alice removed any adjacent pair. The case N=9 can also be shown to be a lost cause by enumeration of Alice’s options.)

## Bayesian Data Analysis [BDA3 - part #2]

Posted in Books, Kids, R, Statistics, University life with tags Andrew Gelman, Bayesian data analysis, Bayesian model choice, Bayesian predictive, finite mixtures, graduate course, hierarchical Bayesian modelling, rats, STAN on March 31, 2014 by xi'an**H**ere is the second part of my review of Gelman et al.’ *Bayesian Data Analysis* (third edition):

“When an iterative simulation algorithm is “tuned” (…) the iterations will not in general converge to the target distribution.” (p.297)

**P**art III covers advanced computation, obviously including MCMC but also model approximations like variational Bayes and expectation propagation (EP), with even a few words on ABC. The novelties in this part are centred at Stan, the language Andrew is developing around Hamiltonian Monte Carlo techniques, a sort of BUGS of the 10′s! (And of course Hamiltonian Monte Carlo techniques themselves. A few (nit)pickings: the book advises important resampling without replacement (p.266) which makes some sense when using a poor importance function but ruins the fundamentals of importance sampling. Plus, no trace of infinite variance importance sampling? of harmonic means and their dangers? In the Metropolis-Hastings algorithm, the proposal is called the jumping rule and denoted by J_{t}, which, besides giving the impression of a Jacobian, seems to allow for time-varying proposals and hence time-inhomogeneous Markov chains, which convergence properties are much hairier. (The warning comes much later, as exemplified in the above quote.) Moving from “burn-in” to “warm-up” to describe the beginning of an MCMC simulation. Being somewhat 90′s about convergence diagnoses (as shown by the references in Section 11.7), although the book also proposes new diagnoses and relies much more on effective sample sizes. Particle filters are evacuated in hardly half-a-page. Maybe because Stan does not handle particle filters. A lack of intuition about the Hamiltonian Monte Carlo algorithms, as the book plunges immediately into a two-page pseudo-code description. Still using physics vocabulary that put *me* (and maybe only *me*) off. Although I appreciated the advice to check analytical gradients against their numerical counterpart.

“In principle there is no limit to the number of levels of variation that can be handled in this way. Bayesian methods provide ready guidance in handling the estimation of the unknown parameters.” (p.381)

**I** also enjoyed reading the part about modes that stand at the boundary of the parameter space (Section 13.2), even though I do not think modes are great summaries in Bayesian frameworks and while I do not see how picking the prior to avoid modes at the boundary avoids the data impacting the prior, *in fine*. The variational Bayes section (13.7) is equally enjoyable, with a proper spelled-out illustration, introducing an unusual feature for Bayesian textbooks. (Except that sampling without replacement is back!) Same comments for the Expectation Propagation (EP) section (13.8) that covers brand new notions. (Will they stand the test of time?!)

“Geometrically, if β-space is thought of as a room, the model implied by classical model selection claims that the true β has certain prior probabilities of being in the room, on the floor, on the walls, in the edge of the room, or in a corner.” (p.368)

**P**art IV is a series of five chapters about regression(s). This is somewhat of a classic, nonetheless Chapter 14 surprised me with an elaborate election example that dabbles in advanced topics like causality and counterfactuals. I did not spot any reference to the *g*-prior or to its intuitive justifications and the chapter mentions the lasso as a regularisation technique, but without any proper definition of this “popular non-Bayesian form of regularisation” (p.368). In French: with not a single equation! Additional novelty may lie in the numerical prior information about the correlations. What is rather crucially (cruelly?) missing though is a clearer processing of variable selection in regression models. I know Andrew opposes any notion of a coefficient being exactly equal to zero, as ridiculed through the above quote, but the book does not reject model selection, so why not in this context?! Chapter 15 on hierarchical extensions stresses the link with exchangeability, once again. With another neat election example justifying the progressive complexification of the model and the cranks and toggles of model building. (I am not certain the reparameterisation advice on p.394 is easily ingested by a newcomer.) The chapters on robustness (Chap. 17) and missing data (Chap. 18) sound slightly less convincing to me, esp. the one about robustness as I never got how to make robustness agree with my Bayesian perspective. The book states “we do not have to abandon Bayesian principles to handle outliers” (p.436), but I would object that the Bayesian paradigm compels us to define an alternative model for those outliers and the way they are produced. One can always resort to a drudging exploration of which subsample of the dataset is at odds with the model but this may be unrealistic for large datasets and further tells us nothing about how to handle those datapoints. The missing data chapter is certainly relevant to such a comprehensive textbook and I liked the survey illustration where the missing data was in fact made of missing questions. However, I felt the multiple imputation part was not well-presented, fearing readers would not understand how to handle it…

“You can use MCMC, normal approximation, variational Bayes, expectation propagation, Stan, or any other method. But your fit must be Bayesian.” (p.517)

**P**art V concentrates the most advanced material, with Chapter 19 being mostly an illustration of a few complex models, slightly superfluous in my opinion, Chapter 20 a very short introduction to functional bases, including a basis selection section (20.2) that implements the “zero coefficient” variable selection principle refuted in the regression chapter(s), and does not go beyond splines (what about wavelets?), Chapter 21 a (quick) coverage of Gaussian processes with the motivating birth-date example (and two mixture datasets I used eons ago…), Chapter 22 a more (too much?) detailed study of finite mixture models, with no coverage of reversible-jump MCMC, and Chapter 23 an entry on Bayesian non-parametrics through Dirichlet processes.

“In practice, for well separated components, it is common to remain stuck in one labelling across all the samples that are collected. One could argue that the Gibbs sampler has failed in such a case.” (p.535)

**T**o get back to mixtures, I liked the quote about the label switching issue above, as I was “one” who argued that the Gibbs sampler fails to converge! The corresponding section seems to favour providing a density estimate for mixture models, rather than component-wise evaluations, but it nonetheless mentions the relabelling by permutation approach (if missing our 2000 JASA paper). The section about inferring on the unknown number of components suggests conducting a regular Gibbs sampler on a model with an upper bound on the number of components and then checking for empty components, an idea I (briefly) considered in the mid-1990′s before the occurrence of RJMCMC. Of course, the prior on the components matters and the book suggests using a Dirichlet with fixed sum like 1 on the coefficients for all numbers of components.

“14. Objectivity and subjectivity: discuss the statement `People tend to believe results that support their preconceptions and disbelieve results that surprise them. Bayesian methods tend to encourage this undisciplined mode of thinking.’¨ (p.100)

**O**bviously, this being a third edition begets the question, *what’s up, doc?!,* i.e., what’s new [when compared with the second edition]? Quite a lot, even though I am not enough of a Gelmanian exegist to produce a comparision table. Well, for a starter, David Dunson and Aki Vethtari joined the authorship, mostly contributing to the advanced section on non-parametrics, Gaussian processes, EP algorithms. Then the Hamiltonian Monte Carlo methodology and Stan of course, which is now central to Andrew’s interests. The book does include a short Appendix on running computations in R and in Stan. Further novelties were mentioned above, like the vision of weakly informative priors taking over noninformative priors but I think this edition of *Bayesian Data Analysis* puts more stress on clever and critical model construction and on the fact that it can be done in a Bayesian manner. Hence the insistence on predictive and cross-validation tools. The book may be deemed somewhat short on exercices, providing between 3 and 20 mostly well-developed problems per chapter, often associated with datasets, rather than the less exciting counter-example above. Even though Andrew disagrees and his students at ENSAE this year certainly did not complain, I personally feel a total of 220 exercices is not enough for instructors and self-study readers. (At least, this reduces the number of email requests for solutions! Esp. when 50 of those are solved on the book website.) But this aspect is a minor quip: overall this is truly the reference book for a graduate course on Bayesian statistics and not only Bayesian data analysis.

## Bayesian Data Analysis [BDA3]

Posted in Books, Kids, R, Statistics, University life with tags Andrew Gelman, Bayesian data analysis, Bayesian model choice, Bayesian predictive, finite mixtures, graduate course, hierarchical Bayesian modelling, rats, STAN on March 28, 2014 by xi'an**A**ndrew Gelman and his coauthors, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Don Rubin, have now published the latest edition of their book *Bayesian Data Analysis*. David and Aki are newcomers to the authors’ list, with an extended section on non-linear and non-parametric models. I have been asked by Sam Behseta to write a review of this new edition for JASA (since Sam is now the JASA book review editor). After wondering about my ability to produce an objective review (on the one hand, this is The Competition to Bayesian Essentials!, on the other hand Andrew is a good friend spending the year with me in Paris), I decided to jump for it and write a most subjective review, with the help of Clara Grazian who was Andrew’s teaching assistant this year in Paris and maybe some of my Master students who took Andrew’s course. The second edition was reviewed in the September 2004 issue of JASA and we now stand ten years later with an even more impressive textbook. Which truly what Bayesian data analysis should be.

**T**his edition has five parts, Fundamentals of Bayesian Inference, Fundamentals of Bayesian Data Analysis, Advanced Computation, Regression Models, and Non-linear and Non-parametric Models, plus three appendices. For a total of xiv+662 pages. And a weight of 2.9 pounds (1395g on my kitchen scale!) that makes it hard to carry around in the metro…. I took it to Warwick (and then Nottingham and Oxford and back to Paris) instead.

“

We could avoid the mathematical effort of checking the integrability of the posterior density (…) The result would clearly show the posterior contour drifting off toward infinity.” (p.111)

**W**hile I cannot go into a detailed reading of those 662 pages (!), I want to highlight a few gems. (I already wrote a detailed and critical analysis of Chapter 6 on model checking in that post.) The very first chapter provides all the necessary items for understanding Bayesian Data Analysis without getting bogged in propaganda or pseudo-philosophy. Then the other chapters of the first part unroll in a smooth way, cruising on the B highway… With the unique feature of introducing weakly informative priors (Sections 2.9 and 5.7), like the half-Cauchy distribution on scale parameters. It may not be completely clear how weak a weakly informative prior, but this novel notion is worth including in a textbook. Maybe a mild reproach at this stage: Chapter 5 on hierarchical models is too verbose for my taste, as it essentially focus on the hierarchical linear model. Of course, this is an essential chapter as it links exchangeability, the “atom” of Bayesian reasoning used by de Finetti, with hierarchical models. Still. Another comment on that chapter: it broaches on the topic of improper posteriors by suggesting to run a Markov chain that can exhibit improperness by enjoying an improper behaviour. When it happens as in the quote above, fine!, but there is no guarantee this is always the case! For instance, improperness may be due to regions near zero rather than infinity. And a last barb: there is a dense table (Table 5.4, p.124) that seems to run contrariwise to Andrew’s avowed dislike of tables. I could also object at the idea of a “true prior distribution” (p.128), or comment on the trivia that hierarchical chapters seem to attract rats (as I also included a rat example in the hierarchical Bayes chapter of *Bayesian Choice* and so does the BUGS Book! Hence, a conclusion that Bayesian textbooks are better be avoided by muriphobiacs…)

“Bayes factors do not work well for models that are inherently continuous (…) Because we emphasize continuous families of models rather than discrete choices, Bayes factors are rarely relevant in our approach to Bayesian statistics.” (p.183 & p.193)

**P**art II is about “the creative choices that are required, first to set up a Bayesian model in a complex problem, then to perform the model checking and confidence building that is typically necessary to make posterior inferences scientifically defensible” (p.139). It is certainly one of the strengths of the book that it allows for a critical look at models and tools that are rarely discussed in more theoretical Bayesian books. As detailed in my earlier post on Chapter 6, model checking is strongly advocated, via posterior predictive checks and… posterior predictive p-values, which are at best empirical indicators that something could be wrong, definitely not that everything’s allright! Chapter 7 is the model comparison equivalent of Chapter 6, starting with the predictive density (aka the evidence or the marginal likelihood), but completely bypassing the Bayes factor for information criteria like the Watanabe-Akaike or widely available information criterion (WAIC), and advocating cross-validation, which is empirically satisfying but formally hard to integrate within a full Bayesian perspective. Chapter 8 is about data collection, sample surveys, randomization and related topics, another entry that is missing from most Bayesian textbooks, maybe not that surprising given the research topics of some of the authors. And Chapter 9 is the symmetric in that it focus on the post-modelling step of decision making.

*(Second part of the review to appear on Monday, leaving readers the weekend to recover!)*