Throughover the workshop in Chennai floated (!) the figure of Jean/André Ville, with his inequality generalising Markov’s, who invented martingales. He is not such a well-known figure in France—at least to me!—, despite having led a rather exceptional life, from being a visiting scholar in Berlin (in the Maison académique de Berlin, along with a certain Jean-Paul Sartre) and Vienna in the 1930s, to his wife being (in Berlin) one of the many (disposable and despised) lovers of JP Sartre (to whom an open-minded or clueless Ville later sent his thèse d’université on martingales and collectives, a much more substantial piece of work than the current PhD), to him working with German and Austrian mathematicians and logicians, such as Popper, Gödel, and Wald–who, what a coïncidence!, died in India from a plane crash in 1950 that had left from Chennai–and being impressed enough by the latter to passing an economics degree in the Sorbonne when back in Paris, establishing a minimax result for a zero-sum matrix game with two players, to his counter-example to von Mises’ kollectiv, to his nickname of the King of Counterexamples in the Viennese mathematics seminar, to him operating the first (Bull) computer at the Université de Paris. (Glenn Shafer wrote a detailed accounting of his youth, on which this post is based, up to his thesis defence but a few days from France mobilising for war–where his collegue Wolfgang Doeblin would kill himself the year after, to avoid capture–. With Bernard Bru, Edmond Malinvaud and Alain Trognon among the people who helped.) After the war, he worked several years as a prépa maths teacher before working for a French State electricity companion on signal theory and Monte Carlo methods, and then returning to Université de Paris as a professor in 1957.
Archive for Karl Popper
André ou Jean Ville (1910-1989)
Posted in Books, pictures, Travel, University life with tags 25w5482, Abraham Wald, Alain Trognon, André Ville, Andrey Markov, École Normale Supérieure, Berlin, Bernard Bru, BIRS-CMI, Bull computers, Chennai, Edmond Malinvaud, Emile Borel, George Darmois, Glenn Shafer, history of Monte Carlo, history of statistics, India, Jean Ville, Jean-Paul Sartre, Karl Popper, Kurt Gödel, martingales, Maurice Fréchet, minimax strategy, Monte Carlo methods, Paris, Paul Lévy, plane crash, Richard von Mises, signal theory, Simone de Beauvoir, Sorbonne, supermartingale, two-player game, Université de Paris, Vienna, Ville's inequality, Wolfgang Doeblin, WW II on August 12, 2025 by xi'an[fool’s] gold standard science
Posted in Books, pictures, Travel, University life with tags @ScientistTrump, Bretton Woods, Donald Trump, Executive Order, falsification, gold standard, Karl Popper, misspecified model, Newspeak, polygraph, Stand up for Science, Stand Up To Trump, The New York Times, Trump administration, uncertainty quantification, White House on June 11, 2025 by xi'an
In this new presidential order of 23 May 2025, Trump pretends to
“restore the scientific integrity policies of my first Administration and ensures that agencies practice data transparency, acknowledge relevant scientific uncertainties, are transparent about the assumptions and likelihood of scenarios used, approach scientific findings objectively, and communicate scientific data accurately”
repeating his goal in
“restoring a gold standard for science to ensure that federally funded research is transparent, rigorous, and impactful, and that Federal decisions are informed by the most credible, reliable, and impartial scientific evidence available”
where
““Weight of scientific evidence” means an approach to scientific evaluation in which each piece of relevant information is considered based on its quality and relevance, and then transparently integrated with other relevant information to inform the scientific evaluation prior to making a judgment about the scientific evaluation. Quality and relevance determinations, at a minimum, should include consideration of study design, fitness for purpose, replicability, peer review, and transparency and reliability of data.”
While the order that
“science [in a federal agency should be] conducted in a manner that is:
(i) reproducible;
(ii) transparent;
(iii) communicative of error and uncertainty;
(iv) collaborative and interdisciplinary;
(v) skeptical of its findings and assumptions;
(vi) structured for falsifiability of hypotheses;
(vii) subject to unbiased peer review;
(viii) accepting of negative results as positive outcomes; and
(ix) without conflicts of interest”
sounds nice and dandy, incl. even a Popperian item!—while I highly doubt the Agent Orange has ever read anything from the author of Open society and its enemies—as well as an assessment of uncertainty and a critical look at the role of models—as if we were not, as a whole, following or trying to follow these tenets!—, the true intent of this order is to submit all research produced by federal agents and federally funded researchers to a vetting by political appointees before submission to a (vetted) scientific journal. As already been put into practice in some Departments. The rosy terms that set how science should be done are turned tupsy-turvy to the Trump administration Newspeak, while the purges in said administration render quality control more illusory than ever… Even the use of the term Gold Standard in a US policy declaration shows how little Trump understands about the term, given the USA abandoned at least twice the gold standard, in 1933 and 1978.
A few days after I wrote this piece, the New York Times published an article pointing out the above (in better terms) and reporting on an open letter from Stand Up for Science signalling the dreadful consequences of the executive order. With a primary correction to the above picture. And the central message that
We view this Executive Order as an escalation of the ongoing assault on science. The first six sections employ common scientific language to spell out a “gold standard” for science that would not strengthen science, but instead would introduce stifling limits on intellectual freedom in our Nation’s laboratories and federal funding agencies. Notably, the order comes from an administration that has already defunded areas of research they do not agree with, pushed vaccine misinformation despite widespread evidence, lied about the impacts of climate change, and incorrectly defined sex determination as binary, when biology proves it is not, in their own Executive Order. Throughout the document, scientific language is hijacked, and ideas are turned on their heads.
And then Andrew decided to discuss its ridiculness on 03 June and again on 03 June. (Which made me realize polygraphs are still used by US law enforcement agencies!)
10 great ideas about chance [book preview]
Posted in Books, pictures, Statistics, University life with tags Abraham Wald, Alan Turing, Allais' paradox, Alonzo Church, Andrei Kolmogorov, BFF4, book review, Borel-Kolmogorov paradox, Brian Skyrms, Bruno de Finetti, Cardano's formula, CHANCE, David Hume, Dutch book argument, equiprobability, exchangeability, Frank Ramsey, gambling, Gerolamo Cardano, Henri Poincaré, heuristics, Jakob Bernoulli, John Maynard Keynes, John von Neumann, Karl Popper, Martin-Löf, measure theory, p-values, Persi Diaconis, Pierre Simon Laplace, PUP, Radon-Nikodym Theorem, randomness, Richard von Mises, sufficiency, Thomas Bayes, Venn diagram 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!]
latest issue of Significance
Posted in Statistics with tags Bayesian data analysis, birthrate, Karl Popper, Royal Statistical Society, Significance on March 20, 2017 by xi'anThe latest issue of Significance is bursting with exciting articles and it is a shame I do not receive it any longer (not that 
I stopped subscribing to the RSS or the ASA, but it simply does not get delivered to my address!). For instance, a tribune by Tom Nicolls (from whom I borrowed this issue for the weekend!) on his recent assessment of false positive in brain imaging [I covered in a blog entry a few months ago] when checking the cluster inference and the returned p-values. 
And the British equivalent of Gelman et al. book cover on the seasonality of births in England and Wales, albeit witout a processing of the raw data and without mention being made of the Gelmanesque analysis: the only major gap in the frequency is around Christmas and New Year, while there is a big jump around September (also there in the New York data).
A neat graph on the visits to four feeders by five species of birds. A strange figure in Perils of Perception that [which?!] French people believe 31% of the population is Muslim and that they are lacking behind many other countries in terms of statistical literacy. And a rather shallow call to Popper to running decision-making in business statistics.
beyond subjective and objective in Statistics
Posted in Books, Statistics, University life with tags academic journals, Basic and Applied Social Psychology, Dennis Lindley, Error-Statistical philosophy, falsification, frequentist inference, Henri Poincaré, Karl Popper, Keep calm posters, Marie Curie, objective Bayes, p-values, refereeing, reproducible research, subjective versus objective Bayes on August 28, 2015 by xi'an
“At the level of discourse, we would like to move beyond a subjective vs. objective shouting match.” (p.30)
This paper by Andrew Gelman and Christian Hennig calls for the abandonment of the terms objective and subjective in (not solely Bayesian) statistics. And argue that there is more than mere prior information and data to the construction of a statistical analysis. The paper is articulated as the authors’ proposal, followed by four application examples, then a survey of the philosophy of science perspectives on objectivity and subjectivity in statistics and other sciences, next to a study of the subjective and objective aspects of the mainstream statistical streams, concluding with a discussion on the implementation of the proposed move. Continue reading
