Archive for Karl Pearson

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.

a conversation about eugenism at JSM

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , , , , , on July 29, 2020 by xi'an

Following the recent debate on Fisher’s involvement in eugenics (and the renaming of the R.A. Fisher Award and Lectureship into the COPSS Distinguished Achievement Award and Lectureship), the ASA is running a JSM round table on Eugenics and its connections with statistics, to which I had been invited, along with Scarlett BellamyDavid Bellhouse, and David Cutler. The discussion is planned on 06 August at 3pm (ET, i.e., 7GMT) and here is the abstract:

The development of eugenics and modern statistical theory are inextricably entwined in history.  Their evolution was guided by the culture and societal values of scholars (and the ruling class) of their time through and including today.  Motivated by current-day societal reckonings of systemic injustice and inequity, this roundtable panel explores the role of prominent statisticians and of statistics more broadly in the development of eugenics at its inception and over the past century.  Leveraging a diverse panel, the discussions seek to shed light on how eugenics and statistics – despite their entangled past — have now severed, continue to have presence in ways that affect our lives and aspirations.

It is actually rather unclear to me why I was invited at the table, apart from my amateur interest in the history of statistics. On a highly personal level, I remember being introduced to Galton’s racial theories during my first course on probability, in 1982, by Prof Ogier, who always used historical anecdotes to enliven his lectures, like Galton trying to measure women mensurations during his South Africa expedition. Lectures that took place in the INSEE building, boulevard Adolphe Pinard in Paris, with said Adolphe Pinard being a founding member of the French Eugenics Society in 1913.

down with Galton (and Pearson and Fisher…)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on July 22, 2019 by xi'an


In the last issue of Significance, which I read in Warwick prior to the conference, there is a most interesting article on Galton’s eugenics, his heritage at University College London (UCL), and the overall trouble with honouring prominent figures of the past with memorials like named building or lectures… The starting point of this debate is a protest from some UCL students and faculty about UCL having a lecture room named after the late Francis Galton who was a professor there. Who further donated at his death most of his fortune to the university towards creating a professorship in eugenics. The protests are about Galton’s involvement in the eugenics movement of the late 18th and early 19th century. As well as professing racist opinions.

My first reaction after reading about these protests was why not?! Named places or lectures, as well as statues and other memorials, have a limited utility, especially when the named person is long dead and they certainly do not contribute in making a scientific theory [associated with the said individual] more appealing or more valid. And since “humans are [only] humans”, to quote Stephen Stigler speaking in this article, it is unrealistic to expect great scientists to be perfect, the more if one multiplies the codes for ethical or acceptable behaviours across ages and cultures. It is also more rational to use amphitheater MS.02 and lecture room AC.18 rather than associate them with one name chosen out of many alumni’s or former professors’.

Predictably, another reaction of mine was why bother?!, as removing Galton’s name from the items it is attached to is highly unlikely to change current views on eugenism or racism. On the opposite, it seems to detract from opposing the present versions of these ideologies. As some recent proposals linking genes and some form of academic success. Another of my (multiple) reactions was that as stated in the article these views of Galton’s reflected upon the views and prejudices of the time, when the notions of races and inequalities between races (as well as genders and social classes) were almost universally accepted, including in scientific publications like the proceedings of the Royal Society and Nature. When Karl Pearson launched the Annals of Eugenics in 1925 (after he started Biometrika) with the very purpose of establishing a scientific basis for eugenics. (An editorship that Ronald Fisher would later take over, along with his views on the differences between races, believing that “human groups differ profoundly in their innate capacity for intellectual and emotional development”.) Starting from these prejudiced views, Galton set up a scientific and statistical approach to support them, by accumulating data and possibly modifying some of these views. But without much empathy for the consequences, as shown in this terrible quote I found when looking for more material:

“I should feel but little compassion if I saw all the Damaras in the hand of a slave-owner, for they could hardly become more wretched than they are now…”

As it happens, my first exposure to Galton was in my first probability course at ENSAE when a terrific professor was peppering his lectures with historical anecdotes and used to mention Galton’s data-gathering trip to Namibia, literally measure local inhabitants towards his physiognomical views , also reflected in the above attempt of his to superpose photographs to achieve the “ideal” thief…

The Seven Pillars of Statistical Wisdom [book review]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , on June 10, 2017 by xi'an

I remember quite well attending the ASA Presidential address of Stephen Stigler at JSM 2014, Boston, on the seven pillars of statistical wisdom. In connection with T.E. Lawrence’s 1926 book. Itself in connection with Proverbs IX:1. Unfortunately wrongly translated as seven pillars rather than seven sages.

As pointed out in the Acknowledgements section, the book came prior to the address by several years. I found it immensely enjoyable, first for putting the field in a (historical and) coherent perspective through those seven pillars, second for exposing new facts and curios about the history of statistics, third because of a literary style one would wish to see more often in scholarly texts and of a most pleasant design (and the list of reasons could go on for quite a while, one being the several references to Jorge Luis Borges!). But the main reason is to highlight the unified nature of Statistics and the reasons why it does not constitute a subfield of either Mathematics or Computer Science. In these days where centrifugal forces threaten to split the field into seven or more disciplines, the message is welcome and urgent.

Here are Stephen’s pillars (some comments being already there in the post I wrote after the address):

  1. aggregation, which leads to gain information by throwing away information, aka the sufficiency principle. One (of several) remarkable story in this section is the attempt by Francis Galton, never lacking in imagination, to visualise the average man or woman by superimposing the pictures of several people of a given group. In 1870!
  2. information accumulating at the √n rate, aka precision of statistical estimates, aka CLT confidence [quoting  de Moivre at the core of this discovery]. Another nice story is Newton’s wardenship of the English Mint, with musing about [his] potential exploiting this concentration to cheat the Mint and remain undetected!
  3. likelihood as the right calibration of the amount of information brought by a dataset [including Bayes’ essay as an answer to Hume and Laplace’s tests] and by Fisher in possible the most impressive single-handed advance in our field;
  4. intercomparison [i.e. scaling procedures from variability within the data, sample variation], from Student’s [a.k.a., Gosset‘s] t-test, better understood and advertised by Fisher than by the author, and eventually leading to the bootstrap;
  5. regression [linked with Darwin’s evolution of species, albeit paradoxically, as Darwin claimed to have faith in nothing but the irrelevant Rule of Three, a challenging consequence of this theory being an unobserved increase in trait variability across generations] exposed by Darwin’s cousin Galton [with a detailed and exhilarating entry on the quincunx!] as conditional expectation, hence as a true Bayesian tool, the Bayesian approach being more specifically addressed in (on?) this pillar;
  6. design of experiments [re-enters Fisher, with his revolutionary vision of changing all factors in Latin square designs], with an fascinating insert on the 18th Century French Loterie,  which by 1811, i.e., during the Napoleonic wars, provided 4% of the national budget!;
  7. residuals which again relate to Darwin, Laplace, but also Yule’s first multiple regression (in 1899), Fisher’s introduction of parametric models, and Pearson’s χ² test. Plus Nightingale’s diagrams that never cease to impress me.

The conclusion of the book revisits the seven pillars to ascertain the nature and potential need for an eight pillar.  It is somewhat pessimistic, at least my reading of it was, as it cannot (and presumably does not want to) produce any direction about this new pillar and hence about the capacity of the field of statistics to handle in-coming challenges and competition. With some amount of exaggeration (!) I do hope the analogy of the seven pillars that raises in me the image of the beautiful ruins of a Greek temple atop a Sicilian hill, in the setting sun, with little known about its original purpose, remains a mere analogy and does not extend to predict the future of the field! By its very nature, this wonderful book is about foundations of Statistics and therefore much more set in the past and on past advances than on the present, but those foundations need to move, grow, and be nurtured if the field is not to become a field of ruins, a methodology of the past!

estimating mixtures by polynomials

Posted in Books, Statistics, University life with tags , , , , , , , on April 7, 2016 by xi'an

mixture with unknown meansSida Wang, Arun Tejasvi, and Chaganty Percy Liang have just arXived a paper about using the method of moments to estimate mixtures of distributions. Method that was introduced (?) by Pearson in 1894 for a Gaussian mixture and crab data. And studied in fair details by Bruce Lindsay and his co-authors, including his book, which makes it the more surprising that Bruce’s work is not mentioned at all in the paper. In particular the 1989 Annals of Statistics paper which connects the number of components with the rank of a moment matrix in exponential family and which made a strong impression on me at the time, just when I was starting to work on mixtures. The current paper addresses more specifically the combinatoric difficulty of solving the moment equation. The solution proceeds via a relaxed convex optimisation problem involving a moment matrix, the relaxation removing the rank condition that identifies the parameters of the mixture. While I am no expert in the resolution of the associated eigenvalue problem (Algorithm 1), I wonder at (i) the existence and convergence of a solution when using empirical moments. And (ii) the impact of the choice of the moment equations, on both existence and efficiency of the moment method. It is clearly not invariant by reparameterisation, hence parameterisation matters. It is even unclear to me how many terms should be used in the resolution: if a single dimension is acceptable, determining this dimension may prove a complex issue.