## out-standing scientist

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , on November 12, 2021 by xi'an

I noticed quite recently that the [Nature] journal Heredity [managed by the Genetics Society] had published an historical / opinion piece on Ronald Fisher and his views on eugenics and race. The authors are all trustees of the Fisher Memorial Trust. The core of the paper contents was also contained in [one of the authors] Stephen Senn’s talk at the JSM round table (I also took part in) and later at the RSS. This is mostly an attempt at resetting Fisher’s position within the era when he lived, in terms of prevalent racism, nationalism, and imperialism. At the core of these woes was a generalised belief in the superiority of some nations, creeds, human groups, even social classes, over others, that was used as a justification in the tragedies of large scale colonialism, the first World War, systemic racism, Nazism, and widespread forced sterilisations….

More attention to the History of Science is needed, as much by scientists as by historians, and especially by biologists, and this should mean a deliberate attempt to understand the thoughts of the great masters of the past, to see in what circumstances or intellectual milieu their ideas were formed, where they took the wrong turning  track or stopped short of the right.”  R.A. Fisher (1959)

While I am thinking the authors are somewhat stretching the arguments isolating Ronald from the worst manifestations of eugenism and racism, as the concept of “voluntary sterilisation” is more than debatable when applied to patients with limited intellectual abilities, as Fisher considered (in 1943) that the Nazi racial laws “have been successful with the best type of German” (which stands as a fairly stupid statement on so many levels, starting with the one that this racial selection had only started a few years before!) and “that the Party sincerely wished to benefit the German racial stock” (in 1948), my already made point is rather that the general tendency of turning genii into saints is bound to meet with disappointment. (Hence, if we have to stick with them, named lectures, prizes, memorials, &tc., should come with an expiration date!)

## baseless!

Posted in Books, Statistics with tags , , , , , , , , , , on July 13, 2021 by xi'an

## 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.

## hard birthday problem

Posted in Books, Kids, R, Statistics with tags , , , , , , , , , on February 4, 2021 by xi'an

Click to access birthday.pdf

From an X validated question, found that WordPress now allows for direct link to pdf documents, like the above paper by my old friend Anirban Das Gupta! The question is about estimating a number M of individuals with N distinct birth dates over a year of T days. After looking around I could not find a simpler representation of the probability for N=r other than (1) in my answer,

$\frac{T!}{(\bar N-r)!}\frac{m!}{T^m} \sum_{(r_1,\ldots,r_m);\\\sum_1^m r_i=r\ \&\\\sum_1^m ir_i=m}1\Big/\prod_{j=1}^m r_j! (j!)^{r_j}$

borrowed from a paper by Fisher et al. (Another Fisher!) Checking Feller leads to the probability (p.102)

${T \choose r}\sum_{\nu=0}^r (-1)^{\nu}{r\choose\nu}\left(1-\frac{T-r+\nu}T \right)^m$

which fits rather nicely simulation frequencies, as shown using

apply(!apply(matrix(sample(1:Nb,T*M,rep=TRUE),T,M),1,duplicated),2,sum)


Further, Feller (1970, pp.103-104) justifies an asymptotic Poisson approximation with parameter$$\lambda(M)=\bar{N}\exp\{-M/\bar N\}$ from which an estimate of$M\$ can be derived. With the birthday problem as illustration (pp.105-106)!

It may be that a completion from N to (R¹,R²,…) where the components are the number of days with one birthdate, two birthdates, &tc. could help design an EM algorithm that would remove the summation in (1) but I did not spend more time on the problem (than finding a SAS approximation to the probability!).

## Don Fraser (1925-2020)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on December 24, 2020 by xi'an

I just received the very sad news that Don Fraser, emeritus professor of statistics at the University of Toronto, passed away this Monday, 21 December 2020. He was a giant of the field, with a unique ability for abstract modelling and he certainly pushed fiducial statistics much further than Fisher ever did. He also developed a theory of structural  inference that came close to objective Bayesian statistics, although he remained quite critical of the Bayesian approach (always in a most gentle manner, as he was a very nice man!). And most significantly contributed to high order asymptotics, to the critical analysis of ancilarity and sufficiency principles, and more beyond. (Statistical Science published a conversation with Don, in 2004, providing more personal views on his career till then.) I met with Don and Nancy rather regularly over the years, as they often attended and talked at (objective) Bayesian meetings, from the 1999 edition in Granada, to the last one in Warwick in 2019. I also remember a most enjoyable barbecue together, along with Ivar Ekeland and his family, during JSM 2018, on Jericho Park Beach, with a magnificent sunset over the Burrard Inlet. Farewell, Don!