Archive for Richard Price
360th anniversary
Posted in Books, University life with tags An Essay towards solving a Problem in the Doctrine of Chances, Bill Bryson, Colbert, Denis de Sallo, Henry Oldenburg, Journal des Sçavans, Louis XIV, Philosophical Transactions of the Royal Society, Richard Price, Royal Society, scientific journals, Thomas Bayes on July 5, 2025 by xi'an
the flawed genius of William Playfair [book review]
Posted in Books, pictures, Statistics, University life with tags 1789, Abraham De Moivre, Adam Smith, bankruptcy, Birmingham, book reviews, capitalism, code breaking, counterfeit, Edinburgh, Edrward Gibbons, Elba, encryption, England, English politics, French Revolution, industrial revolution, Jacobin, Jonathan Strange & Mr Norrell, London, Malthus, Napoléon Bonaparte, Neufchâtel, Paris, Richard Price, Scotland, spy novels, statistical graphics, Thomas Bayes, University of Toronto, Whigs, WIlliam Pitt, William Playfair on March 26, 2024 by xi'an
David Bellhouse has written a new book on the history of statistics, focussing on William Playfair this time (following his fantastic book on Abraham de Moivre). The Flawed Genius of William Playfair (The Story of the Father of Statistical Graphics) got published a few months ago by the University of Toronto Press.
“[Playfair] was an ideas man whose ideas often did not come to fruition; or, when they did, they withered or exploded.” [p.121]
The impressions I retained from reading this detailed account of a perfect unknown (for me) are of a rather unpleasant, unappealing, unsuccessful, fame-seeking, inefficient, short-sighted, self-aggrandising, bigoted, dishonest, man, running from debtors for most of his life, with jail episodes for bankruptcy, while trying to make a living from all sorts of doomed enterprises, short-lived blackmailing attempts, and mediocre books that did not sell to many. Similar to David Bellhouse’s colleague earlier wondering at the appeal of exposing such a rogue character, I am left with this lingering interrogation after finishing the book…
“[Richard] Price liked what Playfair had written. He found [in 1786] Playfair to be “agreeable” and “useful”.” [p.64]
Not that I did not enjoy reading it!, as it gives a most interesting of the era between the 18th and the 19th Centuries, in particular in its detailed narration of the first months of the French Revolution of 1789, and of the impact of the Industrial Revolution on economics and politics as the birth of capitalism. The book abounds in crossing lots of historical characters, like Richard Price (Bayes’s friend who published his most famous paper), Adam Smith (whose book Playfair reprinted with poor additions), Edward Gibbons (whose book along with Smith’s inspired the title of his Inquiry Into the Permanent Causes of the Decline and Fall of Powerful and Wealthy Nations), Thomas Malthus (competing for an annotated edition of Smith’s book), not to mention the political class of Britain at the time. David Bellhouse’s book demonstrates academic and historical excellence, constantly being very detailed, with a wealth of references, documents, and definite support for or against the rumours that accompany the life and deeds of Playfair. (Frankly, rarely a name has been that inappropriate!) This includes for instance the pictures pointing out to his first (?) forged signature [p.140] and the evacuation of the myth of Playfair as a spy for the British Crown—which the Wikipedia page happily reproduces, pointing out the need for an in-depth revision of said page. Similarly, the book delivered a convincing discussion of arguments for and mostly against Playfair “being the key player in the British operation to forge [French] assignats” towards destroying its economy. A lot of the book is touching upon the then novel issue of paper money, which Playfair only and negatively considered through his own (and catastrophic) experiences. At times, the book is almost too scholarly as it makes reading less fluid than was the case his Abraham de Moivre for instance. (And obviously less than in the contemporary Jonathan Strange & Mr. Norrel!) 
It may be that my very relative lack of enthusiasm stems from the realisation that the story of Playfair is overall rather little connected with statistical inference, if not with descriptive statistics (albeit with a complete disregard for the quality and sources of his data), as when publishing a Statistical Breviary on descriptive statistics for a series of countries (and surprisingly sold on Amazon!). Or Statistical Account of the United States of America. And of course for his innovative graphical representations like the one represented on the cover of the book or the pie chart. I feel that the book is much more engaged in Playfair’s contributions to the then nascent science of economics, as for instant about the shallow and mostly misguided views of his’ on banking and running the economy, while conducting his personal finance and investments so disastrously that it negatively advertised against confidence in such views.
On a very personal level, I noticed that some graphs were provided by my friend and statistics historian Stephen Stigler [who also wrote a review of the book] while an analysis of the poor French involved in a coding scam of Playfair about Napoléon’s escape from Elba was by Christian Genest (whom I first met at a statistics conference dinner on the Lac de Neufchâtel in 1986).
[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!]
The [errors in the] error of truth [book review]
Posted in Books, Statistics, University life with tags Abraham De Moivre, Académie des Sciences, book review, Carl Friedrich Gauss, central limit theorem, CHANCE, Edward Simpson, Enlightenment, eugenism, French Revolution, guillotine, Jakob Bernoulli, Karol Wojtyła, Law of Large Numbers, Margaret Thatcher, Marie Curie, Maximilien Robespierre, Ottoman Empire, OUP, Pierre Simon Laplace, Richard Price, Ronald Reagan, St Petersburg, The Bell Curve, Thomas Bayes, typos, Victorian society, Voltaire, wikipedia 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
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)
to de Moivre‘s theorem being given as Taylor’s expansion
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
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),
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.]
an hypothetical chain of transmissions
Posted in Books, Statistics, University life with tags Abbé Morellet, Condorcet, history of statistics, Pierre Simon Laplace, Richard Price, Significance, Thomas Bayes on August 6, 2021 by xi'an
Monte Carlo Markov chains
Posted in Books, Statistics, University life with tags Andrei Kolmogorov, Bayesian Analysis, Bayesian model comparison, book review, CHANCE, Gregor Mendel, iris data, irreducibility, JASA, Jeffreys priors, Kolmogorov axioms, Kolmogorov-Smirnov distance, MCMC, physics, population genetics, pot-pourri, recurrence, Richard Price, Ronald Fisher, Springer-Verlag, textbook, Thomas Bayes, W. Gosset on May 12, 2020 by xi'anDarren Wraith pointed out this (currently free access) Springer book by Massimiliano Bonamente [whose family name means good spirit in Italian] to me for its use of the unusual Monte Carlo Markov chain rendering of MCMC. (Google Trend seems to restrict its use to California!) This is a graduate text for physicists, but one could nonetheless expect more rigour in the processing of the topics. Particularly of the Bayesian topics. Here is a pot-pourri of memorable quotes:
“Two major avenues are available for the assignment of probabilities. One is based on the repetition of the experiments a large number of times under the same conditions, and goes under the name of the frequentist or classical method. The other is based on a more theoretical knowledge of the experiment, but without the experimental requirement, and is referred to as the Bayesian approach.”
“The Bayesian probability is assigned based on a quantitative understanding of the nature of the experiment, and in accord with the Kolmogorov axioms. It is sometimes referred to as empirical probability, in recognition of the fact that sometimes the probability of an event is assigned based upon a practical knowledge of the experiment, although without the classical requirement of repeating the experiment for a large number of times. This method is named after the Rev. Thomas Bayes, who pioneered the development of the theory of probability.”
“The likelihood P(B/A) represents the probability of making the measurement B given that the model A is a correct description of the experiment.”
“…a uniform distribution is normally the logical assumption in the absence of other information.”
“The Gaussian distribution can be considered as a special case of the binomial, when the number of tries is sufficiently large.”
“This clearly does not mean that the Poisson distribution has no variance—in that case, it would not be a random variable!”
“The method of moments therefore returns unbiased estimates for the mean and variance of every distribution in the case of a large number of measurements.”
“The great advantage of the Gibbs sampler is the fact that the acceptance is 100 %, since there is no rejection of candidates for the Markov chain, unlike the case of the Metropolis–Hastings algorithm.”
Let me then point out (or just whine about!) the book using “statistical independence” for plain independence, the use of / rather than Jeffreys’ | for conditioning (and sometimes forgetting \ in some LaTeX formulas), the confusion between events and random variables, esp. when computing the posterior distribution, between models and parameter values, the reliance on discrete probability for continuous settings, as in the Markov chain chapter, confusing density and probability, using Mendel’s pea data without mentioning the unlikely fit to the expected values (or, as put more subtly by Fisher (1936), “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations”), presenting Fisher’s and Anderson’s Iris data [a motive for rejection when George was JASA editor!] as a “a new classic experiment”, mentioning Pearson but not Lee for the data in the 1903 Biometrika paper “On the laws of inheritance in man” (and woman!), and not accounting for the discrete nature of this data in the linear regression chapter, the three page derivation of the Gaussian distribution from a Taylor expansion of the Binomial pmf obtained by differentiating in the integer argument, spending endless pages on deriving standard properties of classical distributions, this appalling mess of adding over the conditioning atoms with no normalisation in a Poisson experiment
botching the proof of the CLT, which is treated before the Law of Large Numbers, restricting maximum likelihood estimation to the Gaussian and Poisson cases and muddling its meaning by discussing unbiasedness, confusing a drifted Poisson random variable with a drift on its parameter, as well as using the pmf of the Poisson to define an area under the curve (Fig. 5.2), sweeping the improperty of a constant prior under the carpet, defining a null hypothesis as a range of values for a summary statistic, no mention of Bayesian perspectives in the hypothesis testing, model comparison, and regression chapters, having one-dimensional case chapters followed by two-dimensional case chapters, reducing model comparison to the use of the Kolmogorov-Smirnov test, processing bootstrap and jackknife in the Monte Carlo chapter without a mention of importance sampling, stating recurrence results without assuming irreducibility, motivating MCMC by the intractability of the evidence, resorting to the term link to designate the current value of a Markov chain, incorporating the need for a prior distribution in a terrible description of the Metropolis-Hastings algorithm, including a discrete proof for its stationarity, spending many pages on early 1990’s MCMC convergence tests rather than discussing the adaptive scaling of proposal distributions, the inclusion of numerical tables [in a 2017 book] and turning Bayes (1763) into Bayes and Price (1763), or Student (1908) into Gosset (1908).
[Usual disclaimer about potential self-plagiarism: this post or an edited version of it could possibly appear later in my Books Review section in CHANCE. Unlikely, though!]
Xi'an's Og 