Archive for Thomas Bayes

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.]

an hypothetical chain of transmissions

Posted in Books, Statistics, University life with tags , , , , , , on August 6, 2021 by xi'an

Bayeswashin

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on May 16, 2021 by xi'an

Just heard via ISBA that the Cass Business School of City University London is changing its name to the Bayes Business School “after it was found (!) that some of Sir John Cass’s wealth was obtained through his links to the slave trade.” One of the school buildings is located on Bunhill Row, which leads to Bunhill Fields cemetery where Thomas Bayes (and Richard Price) were buried. And which stands near the Royal Statistical Society building.

“Bayes’ theorem suggests that we get closer to the truth by constantly updating our beliefs in proportion to the weight of new evidence. It is this idea – not only the person – that is the motivation behind adopting this name.”

While it is a notable recognition of the field that Thomas Bayes was selected by [some members of] the City community, I hope the name will not become a registered trademark! And ponder the relevance of naming schools, buildings, prizes, whatever after individuals who should remain mere mortals rather than carrying the larger-than-life burden of representing ideals and values. And the irony of having a business school named after someone who never worked, being financially wealthy by inheritance (from his Sheffield cutler ancestors).  Or of promoting diversity through a religious zealot leaning towards Arianism.

“In Bayes Business School, we believe we now have a name that reflects who we are and the values we hold. Even though Bayes lived a long time ago, his ideas and his name are very much connected to the future rather than the past.”

Fisher, Bayes, and predictive Bayesian inference [seminar]

Posted in Statistics with tags , , , , , , , , , on April 4, 2021 by xi'an

An interesting Foundations of Probability seminar at Rutgers University this Monday, at 4:30ET, 8:30GMT, by Sandy Zabell (the password is Angelina’s birthdate):

R. A. Fisher is usually perceived to have been a staunch critic of the Bayesian approach to statistics, yet his last book (Statistical Methods and Scientific Inference, 1956) is much closer in spirit to the Bayesian approach than the frequentist theories of Neyman and Pearson.  This mismatch between perception and reality is best understood as an evolution in Fisher’s views over the course of his life.  In my talk I will discuss Fisher’s initial and harsh criticism of “inverse probability”, his subsequent advocacy of fiducial inference starting in 1930, and his admiration for Bayes expressed in his 1956 book.  Several of the examples Fisher discusses there are best understood when viewed against the backdrop of earlier controversies and antagonisms.

probability that a vaccinated person is shielded from COVID-19?

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

Over my flight to Montpellier last week, I read an arXival on a Bayesian analysis of the vaccine efficiency. Whose full title is “What is the probability that a vaccinated person is shielded from Covid-19? A Bayesian MCMC based reanalysis of published data with emphasis on what should be reported as `efficacy'”, by Giulio D’Agostini and Alfredo Esposito. In short I was not particularly impressed.

“But the real point we wish to highlight, given the spread of distributions, is that we do not have enough data for drawing sound conclusion.”

The reason for this lack of enthusiasm on my side is that, while the authors’ criticism of an excessive precision in Pfizer, Moderna, or AstraZeneca press releases is appropriate, given the published confidence intervals are not claiming the same precision, a Bayesian reanalysis of the published outcome of their respective vaccine trial outcomes does not show much, simply because there is awfully little data, essentially two to four Binomial-like outcomes. Without further data, the modelling is one of a simple graph of Binomial observations, with two or three probability parameters, which results in a very standard Bayesian analysis that does depend on the modelling choices being made, from a highly unrealistic assumption of homogeneity throughout the population(s) tested for the vaccine(s), to a lack of hyperparameters that could have been shared between vaccinated populations. Parts of the arXival are unrelated and unnecessary, like the highly detailed MCMC algorithm for simulating the posterior (incl. JAGS code) to the reminiscence of Bayes’ and Laplace’s early rendering of inverse probability. (I find both interesting and revealing that arXiv, just like medRxiv, posts a warning on top of COVID related preprints.)

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