Archive for book review

10 great ideas about chance [book preview]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on November 13, 2017 by xi'an

[As I happened to be a reviewer of this book by Persi Diaconis and Brian Skyrms, I had the opportunity (and privilege!) to go through its earlier version. Here are the [edited] comments I sent back to PUP and the authors about this earlier version. All in  all, a terrific book!!!]

The historical introduction (“measurement”) of this book is most interesting, especially its analogy of chance with length. I would have appreciated a connection earlier than Cardano, like some of the Greek philosophers even though I gladly discovered there that Cardano was not only responsible for the closed form solutions to the third degree equation. I would also have liked to see more comments on the vexing issue of equiprobability: we all spend (if not waste) hours in the classroom explaining to (or arguing with) students why their solution is not correct. And they sometimes never get it! [And we sometimes get it wrong as well..!] Why is such a simple concept so hard to explicit? In short, but this is nothing but a personal choice, I would have made the chapter more conceptual and less chronologically historical.

“Coherence is again a question of consistent evaluations of a betting arrangement that can be implemented in alternative ways.” (p.46)

The second chapter, about Frank Ramsey, is interesting, if only because it puts this “man of genius” back under the spotlight when he has all but been forgotten. (At least in my circles.) And for joining probability and utility together. And for postulating that probability can be derived from expectations rather than the opposite. Even though betting or gambling has a (negative) stigma in many cultures. At least gambling for money, since most of our actions involve some degree of betting. But not in a rational or reasoned manner. (Of course, this is not a mathematical but rather a psychological objection.) Further, the justification through betting is somewhat tautological in that it assumes probabilities are true probabilities from the start. For instance, the Dutch book example on p.39 produces a gain of .2 only if the probabilities are correct.

> gain=rep(0,1e4)
> for (t in 1:1e4){
+ p=rexp(3);p=p/sum(p)
+ gain[t]=(p[1]*(1-.6)+p[2]*(1-.2)+p[3]*(.9-1))/sum(p)}
> hist(gain)

As I made it clear at the BFF4 conference last Spring, I now realise I have never really adhered to the Dutch book argument. This may be why I find the chapter somewhat unbalanced with not enough written on utilities and too much on Dutch books.

“The force of accumulating evidence made it less and less plausible to hold that subjective probability is, in general, approximate psychology.” (p.55)

A chapter on “psychology” may come as a surprise, but I feel a posteriori that it is appropriate. Most of it is about the Allais paradox. Plus entries on Ellesberg’s distinction between risk and uncertainty, with only the former being quantifiable by “objective” probabilities. And on Tversky’s and Kahneman’s distinction between heuristics, and the framing effect, i.e., how the way propositions are expressed impacts the choice of decision makers. However, it is leaving me unclear about the conclusion that the fact that people behave irrationally should not prevent a reliance on utility theory. Unclear because when taking actions involving other actors their potentially irrational choices should also be taken into account. (This is mostly nitpicking.)

“This is Bernoulli’s swindle. Try to make it precise and it falls apart. The conditional probabilities go in different directions, the desired intervals are of different quantities, and the desired probabilities are different probabilities.” (p.66)

The next chapter (“frequency”) is about Bernoulli’s Law of Large numbers and the stabilisation of frequencies, with von Mises making it the basis of his approach to probability. And Birkhoff’s extension which is capital for the development of stochastic processes. And later for MCMC. I like the notions of “disreputable twin” (p.63) and “Bernoulli’s swindle” about the idea that “chance is frequency”. The authors call the identification of probabilities as limits of frequencies Bernoulli‘s swindle, because it cannot handle zero probability events. With a nice link with the testing fallacy of equating rejection of the null with acceptance of the alternative. And an interesting description as to how Venn perceived the fallacy but could not overcome it: “If Venn’s theory appears to be full of holes, it is to his credit that he saw them himself.” The description of von Mises’ Kollectiven [and the welcome intervention of Abraham Wald] clarifies my previous and partial understanding of the notion, although I am unsure it is that clear for all potential readers. I also appreciate the connection with the very notion of randomness which has not yet found I fear a satisfactory definition. This chapter asks more (interesting) questions than it brings answers (to those or others). But enough, this is a brilliant chapter!

“…a random variable, the notion that Kac found mysterious in early expositions of probability theory.” (p.87)

Chapter 5 (“mathematics”) is very important [from my perspective] in that it justifies the necessity to associate measure theory with probability if one wishes to evolve further than urns and dices. To entitle Kolmogorov to posit his axioms of probability. And to define properly conditional probabilities as random variables (as my third students fail to realise). I enjoyed very much reading this chapter, but it may prove difficult to read for readers with no or little background in measure (although some advanced mathematical details have vanished from the published version). Still, this chapter constitutes a strong argument for preserving measure theory courses in graduate programs. As an aside, I find it amazing that mathematicians (even Kac!) had not at first realised the connection between measure theory and probability (p.84), but maybe not so amazing given the difficulty many still have with the notion of conditional probability. (Now, I would have liked to see some description of Borel’s paradox when it is mentioned (p.89).

“Nothing hangs on a flat prior (…) Nothing hangs on a unique quantification of ignorance.” (p.115)

The following chapter (“inverse inference”) is about Thomas Bayes and his posthumous theorem, with an introduction setting the theorem at the centre of the Hume-Price-Bayes triangle. (It is nice that the authors include a picture of the original version of the essay, as the initial title is much more explicit than the published version!) A short coverage, in tune with the fact that Bayes only contributed a twenty-plus paper to the field. And to be logically followed by a second part [formerly another chapter] on Pierre-Simon Laplace, both parts focussing on the selection of prior distributions on the probability of a Binomial (coin tossing) distribution. Emerging into a discussion of the position of statistics within or even outside mathematics. (And the assertion that Fisher was the Einstein of Statistics on p.120 may be disputed by many readers!)

“So it is perfectly legitimate to use Bayes’ mathematics even if we believe that chance does not exist.” (p.124)

The seventh chapter is about Bruno de Finetti with his astounding representation of exchangeable sequences as being mixtures of iid sequences. Defining an implicit prior on the side. While the description sticks to binary events, it gets quickly more advanced with the notion of partial and Markov exchangeability. With the most interesting connection between those exchangeabilities and sufficiency. (I would however disagree with the statement that “Bayes was the father of parametric Bayesian analysis” [p.133] as this is extrapolating too much from the Essay.) My next remark may be non-sensical, but I would have welcomed an entry at the end of the chapter on cases where the exchangeability representation fails, for instance those cases when there is no sufficiency structure to exploit in the model. A bonus to the chapter is a description of Birkhoff’s ergodic theorem “as a generalisation of de Finetti” (p..134-136), plus half a dozen pages of appendices on more technical aspects of de Finetti’s theorem.

“We want random sequences to pass all tests of randomness, with tests being computationally implemented”. (p.151)

The eighth chapter (“algorithmic randomness”) comes (again!) as a surprise as it centres on the character of Per Martin-Löf who is little known in statistics circles. (The chapter starts with a picture of him with the iconic Oberwolfach sculpture in the background.) Martin-Löf’s work concentrates on the notion of randomness, in a mathematical rather than probabilistic sense, and on the algorithmic consequences. I like very much the section on random generators. Including a mention of our old friend RANDU, the 16 planes random generator! This chapter connects with Chapter 4 since von Mises also attempted to define a random sequence. To the point it feels slightly repetitive (for instance Jean Ville is mentioned in rather similar terms in both chapters). Martin-Löf’s central notion is computability, which forces us to visit Turing’s machine. And its role in the undecidability of some logical statements. And Church’s recursive functions. (With a link not exploited here to the notion of probabilistic programming, where one language is actually named Church, after Alonzo Church.) Back to Martin-Löf, (I do not see how his test for randomness can be implemented on a real machine as the whole test requires going through the entire sequence: since this notion connects with von Mises’ Kollektivs, I am missing the point!) And then Kolmororov is brought back with his own notion of complexity (which is also Chaitin’s and Solomonov’s). Overall this is a pretty hard chapter both because of the notions it introduces and because I do not feel it is completely conclusive about the notion(s) of randomness. A side remark about casino hustlers and their “exploitation” of weak random generators: I believe Jeff Rosenthal has a similar if maybe simpler story in his book about Canadian lotteries.

“Does quantum mechanics need a different notion of probability? We think not.” (p.180)

The penultimate chapter is about Boltzmann and the notion of “physical chance”. Or statistical physics. A story that involves Zermelo and Poincaré, And Gibbs, Maxwell and the Ehrenfests. The discussion focus on the definition of probability in a thermodynamic setting, opposing time frequencies to space frequencies. Which requires ergodicity and hence Birkhoff [no surprise, this is about ergodicity!] as well as von Neumann. This reaches a point where conjectures in the theory are yet open. What I always (if presumably naïvely) find fascinating in this topic is the fact that ergodicity operates without requiring randomness. Dynamical systems can enjoy ergodic theorem, while being completely deterministic.) This chapter also discusses quantum mechanics, which main tenet requires probability. Which needs to be defined, from a frequency or a subjective perspective. And the Bernoulli shift that brings us back to random generators. The authors briefly mention the Einstein-Podolsky-Rosen paradox, which sounds more metaphysical than mathematical in my opinion, although they get to great details to explain Bell’s conclusion that quantum theory leads to a mathematical impossibility (but they lost me along the way). Except that we “are left with quantum probabilities” (p.183). And the chapter leaves me still uncertain as to why statistical mechanics carries the label statistical. As it does not seem to involve inference at all.

“If you don’t like calling these ignorance priors on the ground that they may be sharply peaked, call them nondogmatic priors or skeptical priors, because these priors are quite in the spirit of ancient skepticism.” (p.199)

And then the last chapter (“induction”) brings us back to Hume and the 18th Century, where somehow “everything” [including statistics] started! Except that Hume’s strong scepticism (or skepticism) makes induction seemingly impossible. (A perspective with which I agree to some extent, if not to Keynes’ extreme version, when considering for instance financial time series as stationary. And a reason why I do not see the criticisms contained in the Black Swan as pertinent because they savage normality while accepting stationarity.) The chapter rediscusses Bayes’ and Laplace’s contributions to inference as well, challenging Hume’s conclusion of the impossibility to finer. Even though the representation of ignorance is not unique (p.199). And the authors call again for de Finetti’s representation theorem as bypassing the issue of whether or not there is such a thing as chance. And escaping inductive scepticism. (The section about Goodman’s grue hypothesis is somewhat distracting, maybe because I have always found it quite artificial and based on a linguistic pun rather than a logical contradiction.) The part about (Richard) Jeffrey is quite new to me but ends up quite abruptly! Similarly about Popper and his exclusion of induction. From this chapter, I appreciated very much the section on skeptical priors and its analysis from a meta-probabilist perspective.

There is no conclusion to the book, but to end up with a chapter on induction seems quite appropriate. (But there is an appendix as a probability tutorial, mentioning Monte Carlo resolutions. Plus notes on all chapters. And a commented bibliography.) Definitely recommended!

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about Chance!]

blade runner [book review]

Posted in Books, Kids with tags , , , , , , , on November 12, 2017 by xi'an

As the new Blade Runner 2049 film is now out, I realised I have never read the original Philip K Dick novel, Do Androids Dream of Electric Sheep?… So, when I came by it in the wonderful Libreria Marcopolo in Venezia last month, with some time to kill waiting for a free dinner table nearby (and a delicious plate of spaghetti al nero di seppia!), I bought at last the book and read it within a couple evenings. (Plus a trip back from the airport.) While the book is fascinating, both in its construction and in its connection with the first Blade Runner movie, I am somehow disappointed now I have finished it, as I was expecting a somewhat deeper story. [Warning: spoilers to follow!] On the one hand, the post-nuclear California and the hopeless life of those who cannot emigrate to Mars are bleaker and more hopeless than Ridley Scott’s film, with the yearning of Deckard for real animals (rather than his electric sheep) a major focus of the book. And only of the book. For a reason that remains unclear to me, especially because Deckard grows more and more empathic towards androids, and not only towards the ambiguous and fascinating Rachael, while being less and less convinced of his ability to “retire” rogue androids… And of distinguishing between humans and androids. And also because he ends up nurturing a toad he spotted in a deserted location, believing it to be a real animal. The background of the society, its reliance on brainless reality shows and on a religion involving augmented reality, all are great components of the novel, although they feel a bit out-dated fifty years later. (And later than the date the story is supposed to take place.) The human sheltering and helping the fugitive androids is a “chickenhead”, term used in the book for the challenged humans unable to pass the tests for emigrating to Mars. Rather than a robot designer and geek as in the film.

On the other hand, the quasi- or near-humanity of the androids hunted by Deckard is much more better rendered in the film. (Maybe simply because it is a film and hence effortlessly conveys this humanity of actors playing androids. Just like C3PO in Star Wars!) Which connections with expressionisms à la Fritz Lang and noir movies of the 50’s are almost enough to make it a masterpiece. In the book, the androids are much more inconsistent, with repeated hints that they miss some parts of the human experience. There is no lengthy fight between Deckard and the superior (android) Roy. No final existentialist message from the later. And no rescuing of Deckard that makes the android stand ethically (and literally) above Deckard. The only android with some depth is Rachael, albeit with confusing scenes. (If not as confusing as the sequence at the alternative police station that just does not make sense. Unless Deckard himself is an android, a possibility hardly envisioned in the book,.) While Scott’s Blade Runner may seem to hammer its message a wee bit too heavily, it does much better at preserving ambiguity on who is human and who is not, and at the murky moral ground of humans versus androids. In fine, I remain more impacted by the multiple dimensions, perceptions, and uncertainties in Blade Runner.  Than in Philip K Dick’s novel. Still worth reading or re-reading against watching or re-watching these movies…

[Some book covers on this page are taken from a webpage with 23 alternative covers for Do androids dream of electronic sheep?”.]

atheism: a very [very] short introduction [book review]

Posted in Books with tags , , , , , , , , , , , , , , , on November 3, 2017 by xi'an

After the rather disappointing Edge of Reason, I gave a try at Baggini’s very brief introduction to atheism, which is very short. And equally very disappointing. Rather than approaching the topic from a (academic) philosophical perspective, ex nihilo,  and while defending himself from doing so, the author indeed adopts a rather militant tone in trying to justify the arguments and ethics of atheism, setting the approach solely in a defensive opposition to religions. That is, in reverse, as an answer to faiths and creeds. Even when his arguments make complete sense, e.g., in the lack of support for agnosticism against atheism, the link with inductive reasoning (and Hume), and the logical [and obvious] disconnection between morality and religious attitudes.

“…once we accept the inductive method, we should, to be consistent, also accept that it points toward a naturalism that supports atheism…” (p.27)

While he mentions “militant atheism” as a fundamentalist position to be as avoided as the numerous religious versions, I find the whole exercise in this book missing the point of both an intellectual criticism of atheism [in the sense of Kant’s best seller!] and of the VSI series. Again, to define atheism as an answer to religions and to their irrationality is reducing the scope of this philosophical branch to a contrarian posture, rather than independently advancing a rationalist and scientific position on the entropic nature of life and the universe, one that does not require for a purpose or a higher cause. And to try to show it provides better answers to the same questions as those addressed by religions stoops down to their level.

“So it is not the case that atheism follows merely from some shallow commitment to the primacy of scientific inquiry.” (p.77)

The link therein with a philosophical analysis seems so weak that I deem the essay rather belongs to journalosophy. The very short history of atheism and its embarrassed debate on the attributed connections between atheism and some modern era totalitarianisms [found in the last chapter] are an illustration of this divergence from scholarly work. That the author felt the need to include pictures to illustrate his points says it all!

computational methods for numerical analysis with R [book review]

Posted in Books, Kids, pictures, R, Statistics, University life with tags , , , , , , , , , , , , , , , on October 31, 2017 by xi'an

compulysis+R_coverThis is a book by James P. Howard, II, I received from CRC Press for review in CHANCE. (As usual, the customary warning applies: most of this blog post will appear later in my book review column in CHANCE.) It consists in a traditional introduction to numerical analysis with backup from R codes and packages. The early chapters are setting the scenery, from basics on R to notions of numerical errors, before moving to linear algebra, interpolation, optimisation, integration, differentiation, and ODEs. The book comes with a package cmna that reproduces algorithms and testing. While I do not find much originality in the book, given its adherence to simple resolutions of the above topics, I could nonetheless use it for an elementary course in our first year classes. With maybe the exception of the linear algebra chapter that I did not find very helpful.

“…you can have a solution fast, cheap, or correct, provided you only pick two.” (p.27)

The (minor) issue I have with the book and that a potential mathematically keen student could face as well is that there is little in the way of justifying a particular approach to a given numerical problem (as opposed to others) and in characterising the limitations and failures of the presented methods (although this happens from time to time as e.g. for gradient descent, p.191). [Seeping in my Gallic “mal-être”, I am prone to over-criticise methods during classing, to the (increased) despair of my students!, but I also feel that avoiding over-rosy presentations is a good way to avoid later disappointments or even disasters.] In the case of this book, finding [more] ways of detecting would-be disasters would have been nice.

An uninteresting and highly idiosyncratic side comment is that the author preferred the French style for long division to the American one, reminding me of my first exposure to the latter, a few months ago! Another comment from a statistician is that mentioning time series inter- or extra-polation without a statistical model sounds close to anathema! And makes extrapolation a weapon without a cause.

“…we know, a priori, exactly how long the [simulated annealing] process will take since it is a function of the temperature and the cooling rate.” (p.199)

Unsurprisingly, the section on Monte Carlo integration is disappointing for a statistician/probabilistic numericist like me,  as it fails to give a complete enough picture of the methodology. All simulations seem to proceed there from a large enough hypercube. And recommending the “fantastic” (p.171) R function integrate as a default is scary, given the ability of the selected integration bounds to misled its users. Similarly, I feel that the simulated annealing section is not providing enough of a cautionary tale about the highly sensitive impact of cooling rates and absolute temperatures. It is only through the raw output of the algorithm applied to the travelling salesman problem that the novice reader can perceive the impact of some of these factors. (The acceptance bound on the jump (6.9) is incidentally wrongly called a probability on p.199, since it can take values larger than one.)

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE.]

never let me go [book review]

Posted in Books, Kids, pictures, Travel with tags , , , , , , , , , on October 15, 2017 by xi'an

Another chance occurrence led me to read that not so recent book by Kazuo Ishiguro, taking advantage of my short nights while in Warwick. [I wrote this post before the unexpected Nobelisation of the author.] As in earlier novels of his, the strongest feeling is one of melancholia, of things that had been or had supposed to have been and are no longer. Especially the incomparable The Remains of the Day… In the great tradition of the English [teen] novel, this ideal universe is a boarding school, where a group of students bond and grow up, until they face the real world. The story is told with a lot of flashbacks and personal impressions of the single narrator, which made me uncertain of the reality behind her perception and recasting. And of her role and actions within that group, since they always appear more mature and sensible than the others’. The sinister features of this boarding school and the reasons why these children are treated differently emerge very very slowly through the book and the description of their treatment remains unclear till the end of the book. Purposely so. However, once one understands the very reason for their existence, the novels looses its tension, as the perpetual rotation of their interactions gets inconsequential when faced with their short destinies. While one can get attached to the main characters, the doom awaiting them blurs the relevance of their affairs and disputes. Maybe what got me so quickly distanced from the story is the complacency of these characters and the lack of rebellion against their treatment, unless of course it was the ultimate goal of Ishiguro to show that readers, as the “normal” characters in the story, would come to treat the other ones as not completely human… While the final scene about souvenirs and memories sounding like plastic trash trapped on barbed wires seems an easy line, I appreciated the slow construct of the art pieces of Tommy and the maybe too obvious link with their own destiny.

When searching for reviews about this book, I discovered a movie had been made out this book, in 2011, with the same title. And of which I had never heard either..! [Which made me realise the characters were all very young when they died.]

[one of] 99 stories of God

Posted in Books, Kids, pictures with tags , , , , , on August 4, 2017 by xi'an

19

When he was a boy, someone’s great-grandfather told him this story about a traveller in thirteenth-century France.

The traveller met three men pushing wheelbarrows. He asked in what work they were engaged, and he received from them the following three answers.

The first said: I toil from sunrise to sunset and all I receive for my labor is a few francs a day.

The second said: I’m happy enough to wheel this wheelbarrow, for I have not had work for many months and I have a family to feed.

The third said: I am building Chartres Cathedral.

But as a boy he had no idea what a chartres cathedral was.

Joy Williams, ninety-nine stories of God.

[Nitpicking on that sharp little tale: Francs did not become a currency in France until 1360, when it was first coined to attempt to ransom the then king of France, John II, who still died a prisoner in England.]

errors, blunders, and lies [book review]

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , on July 9, 2017 by xi'an

This new book by David Salsburg is the first one in the ASA-CRC Series on Statistical Reasoning in Science and Society. Which explains why I heard about it both from CRC Press [as a suggested material for a review in CHANCE] and from the ASA [as mass emailing]. The name of the author did not ring a bell until I saw the line about his earlier The Lady Tasting Tea book,  a best-seller in the category of “soft [meaning math- and formula-free] introduction to Statistics through picturesque characters”. Which I did not read either [but Bob Carpenter did].

The current book is of the same flavour, albeit with some maths formulas [each preceded by a lengthy apology for using maths and symbols]. The topic is the one advertised in the title, covering statistical errors and the way to take advantage of them, model mis-specification and robustness, and the detection of biases and data massaging. I read the short book in one quick go, waiting for the results of the French Legislative elections, and found no particular appeal in the litany of examples, historical entries, pitfalls, and models I feel I have already read so many times in the story-telling approach to statistics. (Naked Statistics comes to mind.)

It is not that there anything terrible with the book, which is partly based on the author’s own experience in a pharmaceutical company, but it does not seem to bring out any novelty for engaging into the study of statistics or for handling data in a more rational fashion. And I do not see which portion of the readership is targeted by the book, which is too allusive for academics and too academic for a general audience, who is not necessarily fascinated by the finer details of the history (and stories) of the field. As in The Lady Tasting Tea, the chapters constitute a collection of vignettes, rather than a coherent discourse leading to a theory or defending an overall argument. Some chapters are rather poor, like the initial chapter explaining the distinction between lies, blunders, and errors through the story of the measure of the distance from Earth to Sun by observing the transit of Venus, not that the story is uninteresting, far from it!, but I find it lacking in connecting with statistics [e.g., the meaning of a “correct” observation is never explained]. Or the chapter on the Princeton robustness study, where little is explained about the nature of the wrong distributions, which end up as specific contaminations impacting mostly the variance. And some examples are hardly convincing, like those on text analysis (Chapters 13, 14, 15), where there is little backup for using Benford’s law on such short datasets.  Big data is understood only under the focus of large p, small n, which is small data in my opinion! (Not to mention a minor crime de lèse-majesté in calling Pierre-Simon Laplace Simon-Pierre Laplace! I would also have left the Marquis de aside as this title came to him during the Bourbon Restauration, despite him having served Napoléon for his entire reign.) And, as mentioned above, the book contains apologetic mathematics, which never cease to annoy me since apologies are not needed. While the maths formulas are needed.