Archive for book review

humanism [book review]

Posted in Books, Kids with tags , , , , , on January 14, 2018 by xi'an

Along Atheism a very short introduction, I also bought Humanism a very short introduction, as they come by two at the Warwick campus bookstore (!). And here is a very short review.

Written by Stephen Lee, the book is much less irritating than Atheism. In my opinion. Maybe because it is constructed in a much more positive way, maybe because the quotes and illustrations suited me better, maybe because it was another day, or maybe because the stress on the “human” rather than on the “a-” is closer to my own philosophy. Still, the core of the two books is essentially the same, namely a rebuke of the argument that morality only comes as a byproduct of religion(s), and a rather standard processing of arguments for and against the existence of god(s). Plus entries on humanist education and the meaning of life. And a nice cover. Pleasant but not earth-breaking to the point of convincing sceptics.

the shockwave rider [book review]

Posted in Statistics with tags , , , , , , on January 11, 2018 by xi'an

I ordered this book from John Brunner when I found this was the precursor to Neuromancer and the subsequent cyberpunk literature. And after reading it during the Xmas break I am surprised it is not more well-known. Indeed, the plot, the style, the dystopian society in The Shockwave Rider all are highly original, and more “intellectual” than successors like Neuromancer or Snow Crash. Reading this 1975 book forty years later also reveals its premonitory features, from inventing the concept of computer worm (along with a pretty accurate description), to forecasting (or being aware of plans for) cell-phones, the Net, the move to electric cars, and Wikipedia, with the consequence of being always visible for whoever controls the network. The characters are flawed in that they are too charicaturesque, but this is somewhat secondary since the main appeal of the book is to discuss the features of an all-connected world. And the way to recover power to the people against a government controlling the network and the associated data. The time being the 1970’s the resolution via a hippie commune in Northern California (like Eureka!) is a bit outdated and definitely “rosy”, and does not foresee the issue of “digital democracy” being threatened by a strong polarisation into estranged communities, but I still enjoyed the book tremendously. (As a bonus, I got the first edition of the book at a ridiculous price! With this somewhat outdated cover.)

ready player one [book review]

Posted in Books, Kids, pictures with tags , , , , , , , , on January 2, 2018 by xi'an

This book was presumably suggested to me by an Amazon AI based on my previous browsing, and I got intrigued enough by the summary plot and the above cover to order it while in Austin and read it on the way back to Paris. The setting of the story is a catastrolyptic near-future (2044) where gas is a luxury and most of the planet is unemployed and spends its time in a all-immersive free-access virtual reality. Five teenagers join million others in a quest to win a fortune… Against an evil corporation that seeks this fortune and control of the virtual universe. The story revolves around this quest, with some forays in the real world, and a reflection on characters who only know each other via their avatars. Other books based on videogaming come to mind, from Ender’s Game to Neuromancer, to Diamond Age, to REAMDE… But this one is much more focussed on the nature of video-gaming and on the feature of such of a society. I enjoyed the book to the point of staying up late for several evenings in a row, even though the plot is somewhat weak at the societal level, i.e. in describing the economic dynamics of such a society, but setting the games, movies and music themes within the 80’s is obviously catering to readers like me (although I miss a large part of the references). The book was published in 2011, so this is not any recent publication, but there is a movie by Steven Spielberg coming out soon.

about paradoxes

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , on December 5, 2017 by xi'an

An email I received earlier today about statistical paradoxes:

I am a PhD student in biostatistics, and an avid reader of your work. I recently came across this blog post, where you review a text on statistical paradoxes, and I was struck by this section:

“For instance, the author considers the MLE being biased to be a paradox (p.117), while omitting the much more substantial “paradox” of the non-existence of unbiased estimators of most parameters—which simply means unbiasedness is irrelevant. Or the other even more puzzling “paradox” that the secondary MLE derived from the likelihood associated with the distribution of a primary MLE may differ from the primary. (My favourite!)”

I found this section provocative, but I am unclear on the nature of these “paradoxes”. I reviewed my stat inference notes and came across the classic example that there is no unbiased estimator for 1/p w.r.t. a binomial distribution, but I believe you are getting at a much more general result. If it’s not too much trouble, I would sincerely appreciate it if you could point me in the direction of a reference or provide a bit more detail for these two “paradoxes”.

The text is Chang’s Paradoxes in Scientific Inference, which I indeed reviewed negatively. To answer about the bias “paradox”, it is indeed a neglected fact that, while the average of any transform of a sample obviously is an unbiased estimator of its mean (!), the converse does not hold, namely, an arbitrary transform of the model parameter θ is not necessarily enjoying an unbiased estimator. In Lehmann and Casella, Chapter 2, Section 4, this issue is (just slightly) discussed. But essentially, transforms that lead to unbiased estimators are mostly the polynomial transforms of the mean parameters… (This also somewhat connects to a recent X validated question as to why MLEs are not always unbiased. Although the simplest explanation is that the transform of the MLE is the MLE of the transform!) In exponential families, I would deem the range of transforms with unbiased estimators closely related to the collection of functions that allow for inverse Laplace transforms, although I cannot quote a specific result on this hunch.

The other “paradox” is that, if h(X) is the MLE of the model parameter θ for the observable X, the distribution of h(X) has a density different from the density of X and, hence, its maximisation in the parameter θ may differ. An example (my favourite!) is the MLE of ||a||² based on x N(a,I) which is ||x||², a poor estimate, and which (strongly) differs from the MLE of ||a||² based on ||x||², which is close to (1-p/||x||²)²||x||² and (nearly) admissible [as discussed in the Bayesian Choice].

Dan Leno & the Limehouse Golem [book review]

Posted in Books, Travel with tags , , , , , , , , on November 26, 2017 by xi'an

Another book that came to my bedside rather randomly! It is in fact a 1994 book by Peter Ackroyd, not to be confused with Roger Ackroyd, a mystery book by Agatha Christie I remember reading in my teenage years! And takes place in Victorian London, around a woman Elisabeth Cree, who is a music hall celebrity and stands accused of murdering her husband. With the background of a series of gratuitous and inexplicable murders soon attributed to a supernatural creature. Called a golem for its ability to appear and vanish with no witness… There is a great idea in the plot but its implementation is quite tedious, with a plodding style that makes the conclusion a very long wait. This is not helped by Ackroyd borrowing so much from the life of a few well-known historical characters like Karl Marx, George Gissing, Dan Leno and Charles Babbage himself! Simply because they truly existed does not make these characters particularly exciting within the plot. Especially Babbage and his difference engine. (Which was exploited in a much better steampunk novel by William Gibson and Bruce Sterling!) The worst part is when Ackroyd reflects in the book on the engine being a “forerunner of the modern computer”, ruining the whole perspective. As I do not want to get into spoilers about the almost unexpected twists in the conclusion, let me conclude with quotes attributed to Babbage (or followers) about social statistics, for which he had devised the analytical engine.

“To be exactly informed about the lot of humankind (…) is to create the conditions in which it can be ameliorated. We must know before we can understand, and statistic evidence is the surest form of evidence currently in our possession.” (p.113)

“…the errors which arise from unsound reasoning neglecting true data are far more numerous and more durable than those which result from the absence of facts.” (p.119)

 

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?”.]