Archive for Abraham De Moivre

The [errors in the] error of truth [book review]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on August 10, 2021 by xi'an

OUP sent me this book, The error of truth by Steven Osterling, for review. It is a story about the “astonishing” development of quantitative thinking in the past two centuries. Unfortunately, I found it to be one of the worst books I have read on the history of sciences…

To start with the rather obvious part, I find the scholarship behind the book quite shoddy as the author continuously brings in items of historical tidbits to support his overall narrative and sometimes fills gaps on his own. It often feels like the material comes from Wikipedia, despite expressing a critical view of the on-line encyclopedia. The [long] quote below is presumably the most shocking historical blunder, as the terror era marks the climax of the French Revolution, rather than the last fight of the French monarchy. Robespierre was the head of the Jacobins, the most radical revolutionaries at the time, and one of the Assembly members who voted for the execution of Louis XIV, which took place before the Terror. And later started to eliminate his political opponents, until he found himself on the guillotine!

“The monarchy fought back with almost unimaginable savagery. They ordered French troops to carry out a bloody campaign in which many thousands of protesters were killed. Any peasant even remotely suspected of not supporting the government was brutally killed by the soldiers; many were shot at point-blank range. The crackdown’s most intense period was a horrific ten-month Reign of Terror (“la Terreur”) during which the government guillotined untold masses (some estimates are as high as 5,000) of its own citizens as a means to control them. One of the architects of the Reign of Terror was Maximilien Robespierre, a French nobleman and lifelong politician. He explained the government’s slaughter in unbelievable terms, as “justified terror . . . [and] an emanation of virtue” (quoted in Linton 2006). Slowly, however, over the next few years, the people gained control. In the end, many nobles, including King Louis XVI and his wife Marie-Antoinette, were themselves executed by guillotining”

Obviously, this absolute misinterpretation does not matter (very) much for the (hi)story of quantification (and uncertainty assessment), but it demonstrates a lack of expertise of the author. And sap whatever trust one could have in new details he brings to light (life?). As for instance when stating

“Bayes did a lot of his developmental work while tutoring students in local pubs. He was a respected teacher. Taking advantage of his immediate resources (in his circumstance, a billiard table), he taught his theorem to many.”

which does not sound very plausible. I never heard that Bayes had students  or went to pubs or exposed his result to many before its posthumous publication… Or when Voltaire (who died in 1778) is considered as seventeenth-century precursor of the Enlightenment. Or when John Graunt, true member of the Royal Society, is given as a member of the Académie des Sciences. Or when Quetelet is presented as French and as a student of Laplace.

The maths explanations are also puzzling, from the law of large numbers illustrated by six observations, and wrongly expressed (p.54) as

\bar{X}_n+\mu\qquad\text{when}\qquad n\longrightarrow\infty

to  the Saint-Petersbourg paradox being seen as inverse probability, to a botched description of the central limit theorem  (p.59), including the meaningless equation (p.60)

\gamma_n=\frac{2^{2n}}{\pi}\int_0^\pi~\cos^{2n} t\,\text dt

to de Moivre‘s theorem being given as Taylor’s expansion

f(z)=\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(z-a)^2

and as his derivation of the concept of variance, to another botched depiction of the difference between Bayesian and frequentist statistics, incl. the usual horror

P(68.5<70<71.5)=95%

to independence being presented as a non-linear relation (p.111), to the conspicuous absence of Pythagoras in the regression chapter, to attributing to Gauss the concept of a probability density (when Simpson, Bayes, Laplace used it as well), to another highly confusing verbal explanation of densities, including a potential confusion between different representations of a distribution (Fig. 9.6) and the existence of distributions other than the Gaussian distribution, to another error in writing the Gaussian pdf (p.157),

f(x)=\dfrac{e^{-(z-\mu)^2}\big/2\sigma^2}{\sigma\sqrt{2\pi}}

to yet another error in the item response probability (p.301), and.. to completely missing the distinction between the map and the territory, i.e., the probabilistic model and the real world (“Truth”), which may be the most important shortcoming of the book.

The style is somewhat heavy, with many repetitions about the greatness of the characters involved in the story, and some degree of license in bringing them within the narrative of the book. The historical determinism of this narrative is indeed strong, with a tendency to link characters more than they were, and to make them greater than life. Which is a usual drawback of such books, along with the profuse apologies for presenting a few mathematical formulas!

The overall presentation further has a Victorian and conservative flavour in its adoration of great names, an almost exclusive centering on Western Europe, a patriarchal tone (“It was common for them to assist their husbands in some way or another”, p.44; Marie Curie “agreed to the marriage, believing it would help her keep her laboratory position”, p.283), a defense of the empowerment allowed by the Industrial Revolution and of the positive sides of colonialism and of the Western expansion of the USA, including the invention of Coca Cola as a landmark in the march to Progress!, to the fall of the (communist) Eastern Block being attributed to Ronald Reagan, Karol Wojtyła, and Margaret Thatcher, to the Bell Curve being written by respected professors with solid scholarship, if controversial, to missing the Ottoman Enlightenment and being particularly disparaging about the Middle East, to dismissing Galton’s eugenism as a later year misguided enthusiasm (and side-stepping the issue of Pearson’s and Fisher’s eugenic views),

Another recurrent if minor problem is the poor recording of dates and years when introducing an event or a new character. And the quotes referring to the current edition or translation instead of the original year as, e.g., Bernoulli (1954). Or even better!, Bayes and Price (1963).

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

science tidbits

Posted in Books, Kids, pictures, Travel, University life with tags , , , , , , , , , , on January 28, 2018 by xi'an

Several interesting entries in Le Monde Science & Médecine of this week (24 Jan 2018):

  1. This incredible report in the Journal of Ethnobiology of fire-spreading raptors, Black Kite, Whistling Kite, and Brown Falcon, who carry burning material to start fires further away and thus expose rodents and insects. This behaviour was already reported in some Aboriginal myths, as now backed up by independent observations.
  2. A report by Etienne Ghys of the opening of a new CNRS unit in mathematics in… London! The Abraham de Moivre Laboratory is one of the 36 mixed units located outside France to facilitate exchanges and collaborations. In the current case, in collaboration with Imperial. And as a mild antidote to Brexit and its consequences on exchanges between the UK and the EU. (When discussing Martin Hairer’s conference, Etienne forgot to mention his previous affiliation with Warwick.)
  3. A good-will-bad-stats article on the impact of increasing the number of urban bicycle trips to reduce the number of deaths. With the estimation that if 25% of the daily trips over 167 European (and British!) cities were done by bike, 10,000 deaths per year could be avoided! I have not read the original study, but I wonder at the true impact of this increase. If 25% of the commutes are made by bike, the remaining 75% are not and hence use polluting means of transportation. This means more citizens travelling by bike are exposed to the exhausts and fumes of cars, buses, trucks, &tc. Which should see an increase in respiratory diseases, including deaths, rather than a decrease. Unless this measure is associated with banning all exhaust emissions from cities, which does not sound a very likely outcome, even in Paris.
  4. An incoming happening at Cité internationale des Arts in Paris, on Feb 2-3, entitled “we are not the number we believe we are” (in French), based on the universe(s) of Ursula Le Guin who most sadly passed away the day the journal came out.
  5. A diffusion of urban riots in the suburbs of Paris in 2005 that closely follows epidemiological models of flu epidemics, using “a single sociological variable characterizing neighbourhood deprivation”. (Estimation of the SIR model is apparently done by maximum likelihood and model comparison by AIC, given the ODE nature of the models, ABC would have been quite appropriate for a Bayesian modelling!)

JSM 2014, Boston

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , on August 6, 2014 by xi'an

A new Joint Statistical meeting (JSM), first one since JSM 2011 in Miami Beach. After solving [or not] a few issues on the home front (late arrival, one lost bag, morning run, flat in a purely residential area with no grocery store nearby and hence no milk for tea!), I “trekked” to [and then through] the faraway and sprawling Boston Convention Centre and was there in (plenty of) time for Mathias Drton’s Medalion Lecture on linear structural equations. (The room was small and crowded and I was glad to be there early enough!, although there were no Cerberus [Cerberi?] to prevent additional listeners to sit on the ground, as in Washington D.C. a few years ago.) The award was delivered to Mathias by Nancy Reid from Toronto (and reminded me of my Medallion Lecture in exotic Fairbanks ten years ago). I had alas missed Gareth Roberts’ Blackwell Lecture on Rao-Blackwellisation, as I was still in the plane from Paris, trying to cut on my slides and to spot known Icelandic locations from glancing sideways at the movie The Secret Life of Walter Mitty played on my neighbour’s screen. (Vik?)

Mathias started his wide-ranging lecture by linking linear structural models with graphical models and specific features of covariance matrices. I did not spot a motivation for the introduction of confounding factors, a point that always puzzles me in this literature [as I must have repeatedly mentioned here]. The “reality check” slide made me hopeful but it was mostly about causality [another of or the same among my stumbling blocks]… What I have trouble understanding is how much results from the modelling and how much follows from this “reality check”. A novel notion revealed by the talk was the “trek rule“, expressing the covariance between variables as a product of “treks” (sequence of edges) linking those variables. This is not a new notion, introduced by Wright (1921), but it is a very elegant representation of the matrix inversion of (I-Λ) as a power series. Mathias made it sound quite intuitive even though I would have difficulties rephrasing the principle solely from memory! It made me [vaguely] wonder at computational implications for simulation of posterior distributions on covariance matrices. Although I missed the fundamental motivation for those mathematical representations. The last part of the talk was a series of mostly open questions about the maximum likelihood estimation of covariance matrices, from existence to unimodality to likelihood-ratio tests. And an interesting instance of favouring bootstrap subsampling. As in random forests.

I also attended the ASA Presidential address of Stephen Stigler on the seven pillars of statistical wisdom. In connection with T.E. Lawrence’s 1927 book. (Actually, 1922.) Itself in connection with Proverbs IX:1. Unfortunately wrongly translated as seven pillars rather than seven sages.  Here are Stephen’s pillars:

  1. aggregation, which leads to gain information by throwing away information, aka the sufficiency principle [one may wonder at the extension of this principleto non-exponantial families]
  2. information accumulating at the √n rate, aka precision of statistical estimates, aka CLT confidence [quoting our friend de Moivre at the core of this discovery]
  3. likelihood as the right calibration of the amount of information brought by a dataset [including Bayes’ essay]
  4. intercomparison [i.e. scaling procedures from variability within the data, sample variation], eventually leading to the bootstrap
  5. regression [linked with Darwin’s evolution of species, albeit paradoxically] as conditional expectation, hence as a Bayesian tool
  6. design of experiment [enters Fisher, with his revolutionary vision of changing all factors in Latin square designs]
  7. residuals [aka goodness of fit but also ABC!]

Maybe missing the positive impact of the arbitrariness of picking or imposing a statistical model upon an observed dataset. Maybe not as it is somewhat covered by #3, #4 and #7. The reliance on the reproducibility of the data could be the ground on which those pillars stand.

Abraham De Moivre

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , on March 7, 2012 by xi'an

During my week in Roma, I read David Bellhouse’s book on Abraham De Moivre (at night and in the local transportations and even in Via del Corso waiting for my daughter!)… This is a very scholarly piece of work, with many references to original documents, and it may not completely appeal to the general audience: The Baroque Cycle by Neal Stephenson is covering the same period and the rise of the “scientific man” (or Natural Philosopher) in a much more novelised manner, while centering on Newton as its main character and on the earlier Newton-Leibniz dispute, rather than the later Newton-(De Moivre)-Bernoulli dispute. (De Moivre does not appear in the books, at least under his name.)

Bellhouse’s book should however fascinate most academics in that, beside going with the uttermost detail into De Moivre’s contributions to probability, it uncovers the way (mathematical) research was done in the 17th and 18th century England: De Moivre never got an academic position (although he applied for several ones, incl. in Cambridge), in part because he was an emigrated French huguenot (after the revocation of the Édit de Nantes by Louis XIV), and he got a living by tutoring gentry and aristocracy sons in mathematics and accounting. He also was a consultant on annuities. His interactions with other mathematicians of the time was done through coffee-houses, the newly founded Royal Society, and letters. De Moivre published most of his work in the Philosophical Transactions and in self-edited books that he financed by subscriptions. (As a Frenchman, I personally[and so did Jacob Bernoulli!] found puzzling the fact that De Moivre never wrote anything in french but assimilated very quickly into English society.)

Another fascinating aspect of the book is the way English (incl. De Moivre) and Continental mathematicians fought and bickered on the priority of discoveries. Because their papers were rarely and slowly published, and even more slowly distributed throughout Western Europe, they had to rely on private letters for those priority claims. De Moivre’s main achievement is his book, The Doctrine of Chances, which contains among clever binomial derivations on various chance games an occurrence of the central limit theorem for binomial experiments. And the use of generating functions. De Moivre had a suprisingly long life since he died at 87 in London, still giving private lessons as old as 72. Besides being seen as a leading English mathematician, he eventually got recognised by the French Académie Royale des Sciences, if as a foreign member, a few months prior to his death (as well as by the Berlin Academy of Sciences). There is also a small section in the book on the connections between De Moivre and Thomas Bayes (pp. 200-203), although very little is known of their personal interactions. Bayes was close to one of De Moivre’s former students, Phillip Stanhope, and he worked on several of De Moivre’s papers to get entry to the Royal Society. Some open question is whether or not Bayes was ever tutored by De Moivre, although there is no material proof he did. The book also mentions Bayes’ theorem in connection with an comment on The Doctrine of Chances by Hartley (p.191), as if De Moivre had an hand in it or at least a knowledge of it, but this seems unlikely…

In conclusion, this is a highly pleasant and easily readable book on the career of a major mathematician and of one of the founding fathers of probability theory. David Bellhouse is to be congratulated on the scholarship exhibited by this book and on the painstaking pursuit of all historical documents related with De Moivre’s life.