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Monday, September 20, 2021

Jerzy Neyman: A Positive Role Model in the History of Frequentist Statistics

Many of the facts in this blog post come from the biography ‘Neyman’ by Constance Reid. I highly recommend reading this book if you find this blog interesting.

In recent years researchers have become increasingly interested in the relationship between eugenics and statistics, especially focusing on the lives of Francis Galton, Karl Pearson, and Ronald Fisher. Some have gone as far as to argue for a causal relationship between eugenics and frequentist statistics. For example, in a recent book ‘Bernouilli’s Fallacy’, Aubrey Clayton speculates that Fisher’s decision to reject prior probabilities and embrace a frequentist approach was “also at least partly political”. Rejecting prior probabilities, Clayton argues, makes science seem more ‘objective’, which would have helped Ronald Fisher and his predecessors to establish eugenics as a scientific discipline, despite the often-racist conclusions eugenicists reached in their work.

When I was asked to review an early version of Clayton’s book for Columbia University Press, I thought that the main narrative was rather unconvincing, and thought the presented history of frequentist statistics was too one-sided and biased. Authors who link statistics to problematic political views often do not mention equally important figures in the history of frequentist statistics who were in all ways the opposite of Ronald Fisher. In this blog post, I want to briefly discuss the work and life of Jerzy Neyman, for two reasons.


Jerzy Neyman (image from https://statistics.berkeley.edu/people/jerzy-neyman)

First, the focus on Fisher’s role in the history of frequentist statistics is surprising, given that the dominant approach to frequentist statistics used in many scientific disciplines is the Neyman-Pearson approach. If you have ever rejected a null hypothesis because a p-value was smaller than an alpha level, or if you have performed a power analysis, you have used the Neyman-Pearson approach to frequentist statistics, and not the Fisherian approach. Neyman and Fisher disagreed vehemently about their statistical philosophies (in 1961 Neyman published an article titled ‘Silver Jubilee of My Dispute with Fisher’), but it was Neyman’s philosophy that won out and became the default approach to hypothesis testing in most fields[i]. Anyone discussing the history of frequentist hypothesis testing should therefore seriously engage with the work of Jerzy Neyman and Egon Pearson. Their work was not in line with the views of Karl Pearson, Egon's father, nor the views of Fisher. Indeed, it was a great source of satisfaction to Neyman that their seminal 1933 paper was presented to the Royal Society by Karl Pearson, who was hostile and skeptical of the work, and (as Neyman thought) reviewed by Fisher[ii], who strongly disagreed with their philosophy of statistics.

Second, Jerzy Neyman was also the opposite to Fisher in his political viewpoints. Instead of promoting eugenics, Neyman worked to improve the position of those less privileged throughout his life, teaching disadvantaged people in Poland, and creating educational opportunities for Americans at UC Berkeley. He hired David Blackwell, who was the first Black tenured faculty member at UC Berkeley. This is important, because it falsifies the idea put forward by Clayton[iii] that frequentist statistics became the dominant approach in science because the most important scientists who worked on it wanted to pretend their dubious viewpoints were based on ‘objective’ scientific methods.  

I think it is useful to broaden the discussion of the history of statistics, beyond the work by Fisher and Karl Pearson, and credit the work of others[iv] who contributed in at least as important ways to the statistics we use today. I am continually surprised about how few people working outside of statistics even know the name of Jerzy Neyman, even though they regularly use his insights when testing hypotheses. In this blog, I will try to describe his work and life to add some balance to the history of statistics that most people seem to learn about. And more importantly, I hope Jerzy Neyman can be a positive role-model for young frequentist statisticians, who might so far have only been educated about the life of Ronald Fisher.


Neyman’s personal life


Neyman was born in 1894 in Russia, but raised in Poland. After attending the gymnasium, he studied at the University of Kharkov. Initially trying to become an experimental physicist, he was too clumsy with his hands, and switched to conceptual mathematics, in which he concluded his undergraduate in 1917 in politically tumultuous times. In 1919 he met his wife, and they marry in 1920. Ten days later, because of the war between Russia and Poland, Neyman is imprisoned for a short time, and in 1921 flees to a small village to avoid being arrested again, where he obtains food by teaching the children of farmers. He worked for the Agricultural Institute, and then worked at the University in Warsaw. He obtained his doctor’s degree in 1924 at age 30. In September 1925 he was sent to London for a year to learn about the latest developments in statistics from Karl Pearson himself. It is here that he met Egon Pearson, Karl’s son, and a friendship and scientific collaboration starts.

Neyman always spends a lot of time teaching, often at the expense of doing scientific work. He was involved in equal opportunity education in 1918 in Poland, teaching in dimly lit classrooms where the rag he used to wipe the blackboard would sometimes freeze. He always had a weak spot for intellectuals from ‘disadvantaged’ backgrounds. He and his wife were themselves very poor until he moved to UC Berkeley in 1938. In 1929, back in Poland, his wife becomes ill due to their bad living conditions, and the doctor who comes to examine her is so struck by their miserable living conditions he offers the couple stay in his house for the same rent they were paying while he visits France for 6 months. In his letters to Egon Pearson from this time, he often complained that the struggle for existence takes all his time and energy, and that he can not do any scientific work.

Even much later in his life, in 1978, he kept in mind that many people have very little money, and he calls ahead to restaurants to make sure a dinner before a seminar would not cost too much for the students. It is perhaps no surprise that most of his students (and he had many) talk about Neyman with a lot of appreciation. He wasn’t perfect (for example, Erich Lehmann - one of Neyman's students - remarks how he was no longer allowed to teach a class after Lehmann's notes, building on but extending the work by Neyman, became extremely popular – suggesting Neyman was no stranger to envy). But his students were extremely positive about the atmosphere he created in his lab. For example, job applicants were told around 1947 that “there is no discrimination on the basis of age, sex, or race ... authors of joint papers are always listed alphabetically."

Neyman himself often suffered discrimination, sometimes because of his difficulty mastering the English language, sometimes for being Polish (when in Paris a piece of clothing, and ermine wrap, is stolen from their room, the police responds “What can you expect – only Poles live there!”), sometimes because he did not believe in God, and sometimes because his wife was Russian and very emancipated (living independently in Paris as an artist). He was fiercely against discrimination. In 1933, as anti-Semitism is on the rise among students at the university where he works in Poland, he complains to Egon Pearson in a letter that the students are behaving with Jews as Americans do with people of color. In 1941 at UC Berkeley he hired women at a time it was not easy for a woman to get a job in mathematics.  

In 1942, Neyman examined the possibility of hiring David Blackwell, a Black statistician, then still a student. Neyman met him in New York (so that Blackwell does not need to travel to Berkeley at his own expense) and considered Blackwell the best candidate for the job. The wife of a mathematics professor (who was born in the south of the US) learned about the possibility that a Black statistician might be hired, warns she will not invite a Black man to her house, and there was enough concern for the effect the hire would have on the department that Neyman can not make an offer to Blackwell. He is able to get Blackwell to Berkeley in 1953 as a visiting professor, and offers him a tenured job in 1954, making David Blackwell the first tenured faculty member at the University of Berkeley, California. And Neyman did this, even though Blackwell was a Bayesian[v] ;).

In 1963, Neyman travelled to the south of the US and for the first time directly experienced the segregation. Back in Berkeley, a letter is written with a request for contributions for the Southern Christian Leadership Conference (founded by Martin Luther King, Jr. and others), and 4000 copies are printed and shared with colleagues at the university and friends around the country, which brought in more than $3000. He wrote a letter to his friend Harald Cramér that he believed Martin Luther King, Jr. deserved a Nobel Peace Prize (which Cramér forwarded to the chairman of the Nobel Committee, and which he believed might have contributed at least a tiny bit to fact that Martin Luther King, Jr. was awarded the Nobel Prize a year later). Neyman also worked towards the establishment of a Special Scholarships Committee at UC Berkeley with the goal of providing education opportunities to disadvantaged Americans

Neyman was not a pacifist. In the second world war he actively looked for ways he could contribute to the war effort. He is involved in statistical models that compute the optimal spacing of bombs by planes to clear a path across a beach of land mines. (When at a certain moment he needs specifics about the beach, a representative from the military who is not allowed to directly provide this information asks if Neyman has ever been to the seashore in France, to which Neyman replies he has been to Normandy, and the representative answers “Then use that beach!”). But Neyman early and actively opposed the Vietnam war, despite the risk of losing lucrative contracts the Statistical Laboratory had with the Department of Defense. In 1964 he joined a group of people who bought advertisements in local newspapers with a picture of a napalmed Vietnamese child with the quote “The American people will bluntly and plainly call it murder”.


A positive role model


It is important to know the history of a scientific discipline. Histories are complex, and we should resist overly simplistic narratives. If your teacher explains frequentist statistics to you, it is good if they highlight that someone like Fisher had questionable ideas about eugenics. But the early developments in frequentist statistics involved many researchers beyond Fisher[vi], and, luckily, there are many more positive role-models that also deserve to be mentioned - such as Jerzy Neyman. Even though Neyman’s philosophy on statistical inferences forms the basis of how many scientists nowadays test hypotheses, his contributions and personal life are still often not discussed in histories of statistics - an oversight I hope the current blog post can somewhat mitigate. If you want to learn more about the history of statistics through Neyman’s personal life, I highly recommend the biography of Neyman by Constance Reid, which was the source for most of the content of this blog post.

 



[i] See Hacking, 1965: “The mature theory of Neyman and Pearson is very nearly the received theory on testing statistical hypotheses.”

[ii] It turns out, in the biography, that it was not Fisher, but A. C. Aitken, who reviewed the paper positively.

[iii] Clayton’s book seems to be mainly intended as an attempt to persuade readers to become a Bayesian, and not as an accurate analysis of the development of frequentist statistics.

[iv] William Gosset (or 'Student', from 'Student's t-test'), who was the main inspiration for the work by Neyman and Pearson, is another giant in frequentist statistics who does not in any way fit into the narrative that frequentist statistics is tied to eugenics, as his statistical work was motivated by applied research questions in the Guinness brewery. Gosset was a modest man – which is probably why he rarely receives the credit he is due.

[v] When asked about his attitude towards Bayesian statistics in 1979, he answered: “It does not interest me. I am interested in frequencies.” He did note multiple legitimate approaches to statistics exist, and the choice one makes is largely a matter of personal taste. Neyman opposed subjective Bayesian statistics because their use could lead to bad decision procedures, but was very positive about later work by Wald, which inspired Bayesian statistical decision theory.

[vi] For a more nuanced summary of Fisher's life, see https://www.nature.com/articles/s41437-020-00394-6 

 

8 comments:

  1. Thanks Daniel for taking your time and efforts in writing this post. Very interesting and much appreciated. I see a typo error in Neyman birth year.

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  2. An interesting post but misleading in some respects. Neyman desrves praise for his support of David Blackwell but the implication that in this he was somehow different from Fisher is false. Fisher supported and collaborated with many Indian statisticians (see ths Sankhya obituary here http://www.senns.uk/Sankhya_Obit_RAF.pdf) and his doctoral students included CR Rao and the Ghanaian Ebenezer Laing. (It is interesting to note that PV Sukhatme, whose work Fisher liked, studied for a PhD with Neyman and a DSc with Fisher, consistent with the point of view that attitudes to non-European researchers does not really separate them.) Furthermore, Neyman's enthusiasm for communism had its negative side. It proved to be an embarassment for Polish statisticians who had to live the reality of the paradise he imagined.
    As regards significance and hypothesis testing, in my opinion. the difference between Neyman and Pearson and Fisher has little to do with P-values versus rejection but more to do with the role of alternative hypotheses (crucial for Neyman and not needed by Fisher) and conditioning (important for Fisher but less obviously so for Neyman).

    (Small point There is a typo. Neyman was born in 1894. Also, I suppose it is debatable as to whether Bender, Neyman's place of birth, should be described as being in Russia.)

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  4. Thank you for sharing. He deserves more credit.

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  5. Thank you for sharing. He deserves more credit.

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