I'm one season behind in "Only Murders in the Building" and only watched the scene pictured above last night showing Steve Martin with a fish called President William McKinley. Could it be a coincidence that the Fanta-faced phalangist is also catching up on the show, thereby motivating his new found sympathy for McKinley's tariff policy, ... and, and His Orange-ness being flushed down the toilet later in the same episode?
Among the lesser injustices, there is the failure of capitalism to produce the odd item that in my humble opinion would improve life in general, or mine in particular. I've written earlier about the Bialetti Elettrodomestici Macchina Per Pasta. It would be nice if someone brought chervil to my local farmers market. Such market failures don't measure up to the failure of the Soviet state to produce enough copies of the poetry of Osip Mandelstam to satisfy demand.
Which brings me to Penelope Unbound, a novel by Mary Morrissy, published last year by Banshee Press an independent Irish press. The premiss of the novel is simple: What if Norah Barnacle had grown tired of waiting for James Joyce at the train station in Trieste and had been taken home by a good samaritan? From this idea, Morrissy weaves a funny, but very poignant tale that deserves a much wider audience. In particular the novel deserves a U.S. publisher. John Banville wrote an ecstatic review in the Guardian, but this doesn't seem to have been appreciated in America. Why?
Every 20 years or so I am reminded to reread Thorstein Veblen's essay, The Intellectual Pre-Eminence of Jews in Modern Europe, Political Science Quarterly (1919). With the war in Gaza raging and my belated reading of Michael Chabon's novel Moonglow nearly finished, this seemed to be another such moment. The Veblen essay is brilliant not only because it turns all the ambient eugenicist anti-semitic tripe of its time on its head, but because it offers a warning about the consequences to Europe of the Zionist project. Were this project to succeed and Jews were to find a comfortable homeland that allowed them to retreat into their religious heritage and lose their engagement and skepticism about science and society in the rest of the world the loss of their contribution would be a tragedy. Of course this dream is far from realization and for most Zionists opting out of world of science and culture was never the objective. Perhaps now it is time for me to read yet another Veblen opus, his Yale Phd dissertation in philosophy titled, "Ethical Grounds of a Doctrine of Retribution". Unfortunately, to the best of my googling this item appears to be lost in the ozone, just when we need it most.
1. All speech in and around universities should be encrypted.
2. All houses within a one kilometer radius of the home of a
school shooter should be bulldozed.
3. The following ten great ideas of statistics should be canceled:
a. Correlation because Karl Pearson was a eugenicist.
b. Regression because Francis Galton was a eugenicist
c. Likelihood because R.A. Fisher was a eugenicist
d. Likelihood Principle because George Barnard was a communist
e. 0-1 Law because Andrey Kolmogorov was a communist
f. Markov Processes because Andrey Markov was an atheist
g. Gini Coefficient because Corrado Gini was a fascist
h. Exchangeability because Bruno de Finetti was a fascist
i. Causality because Plato was a fascist
j. Time because Martin Heidegger was a fascist
~
~
In a 2021 post Cauchy priors I made a gigantic blunder in misinterpreting a twitter response to a question posed by Victor Chernozhukov about the mean E[X|X+Y] when X is standard Gaussian, and Y is independent and standard Cauchy. I reformulated this as: suppose Y|T ~ N(T,1) and T ~ Cauchy, what is E(T|Y=y)? This is a standard Bayesian problem with the idea of Cauchy priors going back to Jeffreys and explored more recently by Berger and others. My blunder was elementary and involved failing to remember that the normalizing factor for the conditional density was dependent on y. When this was fixed, I get the figure below. To accentuate the flat portion of the posterior mean I've reduced the scale of the Cauchy to be 0.1 rather than 1. The interpretation of figure is quite intuitive: when y is near zero and therefore in agreement with the prior, the posterior mean is aggressively shrunken toward zero. However, when |y| is far from zero, the prior says, "well, that could happen" and the posterior eventually looks indistinguishable from y.
There is a mildly amusing story associated with how I came to revisit this problem. I have been reading a recent JPE paper A/B Testing with Fat Tails that employs Student t priors with low degrees of freedom in an essential way. Having totally forgotten about the previous blog post, I proceeded to investigate how to compute this posterior mean, and not surprisingly my initial attempts faltered a bit, so I started to google around to see what was "out there" in webland. Early on I found a nice paper by Guy Nason that dealt with the case of Student on 3 dfs. It mentioned that there was a 1939 David Kendall paper that treated the Cauchy case. This must have been written when Kendall was still a grad student. It involves some quite exotic complex analysis, and among others cites a 1935 paper by Robert Oppenheimer! If I interpret Nason correctly, the Kendall paper produces a "closed form" expression for the marginal density of a Cauchy mixture of Gaussians. Kendall comments rather drolly that the expression isn't useful for computations because there was no tabulated version of the erfc function for complex arguments. This lack has been rectified in the intervening years, but my attempts in R, and then in Mathematica to check that this Kendall's expression integrated to one failed. Instead, the integral seemed to diverge slowly. I would be grateful for any and all suggestions about this, but I rather expect that it is all lost in the mists of time.
Meanwhile, fortunately, it is easy to cook up a numerical version of the posterior mean solution that I will append here:
# Berger problem
s <- 0.1
f <- function(t,x) dnorm(x-t, sd = 1) * dt(t/s,1)/s
k <- function(x) integrate(f, -Inf,Inf, x = x)$value
g <-function(t,x) t * f(t,x)
h <- function(x) integrate(g, -Inf,Inf, x = x)$value
x <- -100:100/10
m <- x
for(i in 1:length(x)) m[i] <- h(x[i])/k(x[i])
png("Cauchy.png")
plot(x, m, type = "l", xlab = "y", ylab = expression(E~theta|Y==y))
abline(c(0,1),col = 2)
abline(h = 0,col = 2)
dev.off()
I joined Twitter in 2009 in the futile hope that it would lead me to a Korean Taco truck on my first ever visit to LA. It didn't occur to me to tweet until 2021 when I decided that it was time to launch a quixotic attempt to get Bialetti to revive their legendary pasta machine. This failed miserably too, although the Guardian food columnist Racheal Roddy was very nice about it.
Since then I've tweeted a few times always in response to something someone else had written. This led me to wonder why I couldn't bring myself to originate a tweet. The answer to this query appeared to me yesterday in the form of a talk delivered by Frank Ramsey in 1925 that appears as the Epilogue in the collection of Ramsey's papers edited by R.B. Braithwaite titled: "The Foundations of Mathematics"
I've been reading about the Rasch model of item response in educational testing, in preparation for writing a brief section about it for the empirical Bayes book. Eventually, I recalled that Edgeworth had an amusing paper about this sort of thing, from which I quote the final paragraph.
To examiners at least it will be interesting to test the accuracy of the instrument with which they work. The statistical study may beguile the monotony of their task. The " charm severe of numbers " is celebrated by Wordsworth as
"Especially perceived when nature droops
And feeling is suppressed."
The poet is evidently describing in prophetic words words the condition of examiners, and prescribing their solace. More tropically another inspired bard has indicated the paregoric use of an interest in statistics. In one of the beautiful pictures with which Homer has adorned the shield of Achilles, the ploughman of the good old times, as he finishes each furrow, and turns to begin a new one, is presented with a refreshing cup of honey-sweet wine. So they who plough in the modern metaphorical sense, may, in the pauses of their labours, be refreshed with the cup of statistical science, which I have endeavoured to sweeten.
F.Y. Edgeworth (1890) The Element of Chance in Competitive Examinations, JRSS, 664-663.
