a [counter]example of minimaxity

A chance question on X validated made me reconsider about the minimaxity over the weekend. Consider a Geometric G(p) variate X. What is the minimax estimator of p under squared error loss ? I thought it could be obtained via (Beta) conjugate priors, but following Dyubin (1978) the minimax estimator corresponds to a prior with point masses at ¼ and 1, resulting in a constant estimator equal to ¾ everywhere, except when X=0 where it is equal to 1. The actual question used a penalised qaudratic loss, dividing the squared error by p(1-p), which penalizes very strongly errors at p=0,1, and hence suggested an estimator equal to 1 when X=0 and to 0 otherwise. This proves to be the (unique) minimax estimator. With constant risk equal to 1. This reminded me of this fantastic 1984 paper by Georges Casella and Bill Strawderman on the estimation of the normal bounded mean, where the least favourable prior is supported by two atoms if the bound is small enough. Figure 1 in the Negative Binomial extension by Morozov and Syrova (2022) exploits the same principle. (Nothing Orwellian there!) If nothing else, a nice illustration for my Bayesian decision theory course!

the best books of the NYT readers

Two years after Le Monde reported on the list of the 101 favourite novels of [some of] its readers, which I found most fascinating as a sociological entry on said readers, rather than a meaningful ordering of literary monuments (!),  even though it led me to read Damasio’s La Horde du Contrevent, as well as Jean-Philippe Jaworski’s Gagner la Guerre [To the victors go the spoils], The New York Times did something similar to celebrate the Book Review’s 125th anniversary. If on a lesser scale, as it only produces

1. 1. 1. 1. To Kill a Mockingbird by Harper Lee
         2. The Fellowship of the Ring by J.R.R. Tolkien
         3. 1984 by George Orwell
         4. One Hundred Years of Solitude by Gabriel García Márquez
         5. Beloved by Toni Morrison

as the top five books of the last 125th years, Lee’s, Tolkien’s, and Garcia Márquez’s appearing in both lists, if with a different ranking. (The nomination rules were not exactly the same, though, with only novels for Le Monde and only “recent” books and only one per author for the New York Times.) Here is a longer list of the 25 top contenders, from which NYT readers voted [an opportunity I missed!]:

• 1984 by George Orwell
• All the Light We Cannot See by Anthony Doerr
• Beloved by Toni Morrison
• Catch-22 by Joseph Heller
• The Catcher in the Rye by J.D. Salinger
• Charlotte’s Web by E.B. White
• A Confederacy of Dunces by John Kennedy Toole
• The Fellowship of the Ring by J.R.R. Tolkien
• A Fine Balance by Rohinton Mistry
• A Gentleman in Moscow by Amor Towles
• Gone With the Wind by Margaret Mitchell
• The Grapes of Wrath by John Steinbeck
• The Great Gatsby by F. Scott Fitzgerald
• The Handmaid’s Tale by Margaret Atwood
• Harry Potter and the Sorcerer’s Stone by J.K. Rowling
• Infinite Jest by David Foster Wallace
• To Kill a Mockingbird by Harper Lee
• A Little Life by Hanya Yanagihara
• Lolita by Vladimir Nabokov
• Lonesome Dove by Larry McMurtry
• One Hundred Years of Solitude by Gabriel García Márquez
• The Overstory by Richard Powers
• A Prayer for Owen Meany by John Irving
• A Tree Grows in Brooklyn by Betty Smith
• Ulysses by James Joyce

some of which I had never heard of. And not including a single Faulkner’s… Except for One Hundred Years of Solitude, first published as Cien años de soledad, all novels there were originally written in English. Sadly, the number one book, To Kill a Mockingbird, is also one of the most censored by school boards in the USA! (And so are books by Toni Morrison.)

moral [dis]order

“For example, a religiously affiliated college that receives federal grants could fire a professor simply for being gay and still receive those grants. Or federal workers could refuse to process the tax returns of same-sex couples simply because of bigotry against their marriages. It doesn’t stop there. As critics of the bill quickly pointed out, the measure’s broad language — which also protects those who believe that “sexual relations are properly reserved to” heterosexual marriages alone — would permit discrimination against anyone who has sexual relations outside such a marriage. That would appear to include women who have children outside of marriage, a class generally protected by federal law.” The New York Time

An excerpt from this week New York Time Sunday Review editorial about what it qualifies as “a nasty bit of business congressional Republicans call the First Amendment Defense Act.” A bill which first line states to be intended to “prevent discriminatory treatment of any person on the basis of views held with respect to marriage” and which in essence would allow for discriminatory treatment of homosexual and unmarried couples not to be prosecuted. A fine example of Newspeak if any! (Maybe they could also borrow Orwell‘s notion of a Ministry of Love.) Another excerpt of the bill that similarly competes for Newspeak of the Year:

(5) Laws that protect the free exercise of religious beliefs and moral convictions about marriage will encourage private citizens and institutions to demonstrate tolerance for those beliefs and convictions and therefore contribute to a more respectful, diverse, and peaceful society.

This reminded me of a story I was recently told me about a friend of a friend who is currently employed by a Catholic school in Australia and is afraid of being fired if found being pregnant outside of marriage. Which kind of “freedom” is to be defended in such “tolerant” behaviours?!