Archive for Russian mathematicians

the nihilist girl [book review]

Posted in Books, Kids with tags , , , , , , , , , , , , on October 7, 2017 by xi'an

When stopping by an enticing bookstore on Rue Saint-Jacques, in front of La Sorbonne, last July, I came across a book by the mathematician Sofia Kovaleskaya called the nihilist girl. Having never heard of non-mathematical books written by this Russian mathematician whose poster stood in my high school classroom, I bought it (along with other summer reads). And then discovered that besides being a woman of many “firsts”, from getting a PhD at Heidelberg (under Weirstraß) to getting a professor position in Stockholm, to being nominated to a Chair in the Russian Academy of Sciences, she also took an active part in the Commune de Paris, along with many emigrated Russian revolutionaries (or nihilists). Which explains for this book about a nihilist girl leaving everything to follow a revolutionary deported to Siberia. While not autobiographical (Sweden is not Siberia!), the novel contains many aspects inspired from the (amazing if desperately short) life of Sofia Kovaleskaya herself. A most interesting coincidence is that Sofia’s sister, Anna, was engaged for a while to Fyodor Dostoyevsky, whose novel The Demons takes the opposite view on nihilists. (As a feminist and anarchist, Anna took a significant part in the Commune de Paris, to the point of having to flee to Switzerland to escape deportation to New Caledonia, while her husband was sentenced to death.) The book itself is not particularly enjoyable, as being quite naïve in its plot and construction. It is nonetheless a great testimony of the situation of Russia in the 19th Century and of the move of the upper-class liberals towards revolutionary ideals, while the exploited peasant class they wanted to free showed no inclination to join them. I think Dostoyevsky expresses much more clearly this most ambiguous posturing of the cultivated classes at the time, yearning for more freedom and fairness for all, but fearing the Tsarist police, unable to connect with the peasantry, and above all getting a living from revenues produced by their farmlands.

Is Jeffreys’ prior unique?

Posted in Books, Statistics, University life with tags , , , , , on March 3, 2015 by xi'an

“A striking characterisation showing the central importance of Fisher’s information in a differential framework is due to Cencov (1972), who shows that it is the only invariant Riemannian metric under symmetry conditions.” N. Polson, PhD Thesis, University of Nottingham, 1988

Following a discussion on Cross Validated, I wonder whether or not the affirmation that Jeffreys’ prior was the only prior construction rule that remains invariant under arbitrary (if smooth enough) reparameterisation. In the discussion, Paulo Marques mentioned Nikolaj Nikolaevič Čencov’s book, Statistical Decision Rules and Optimal Inference, Russian book from 1972, of which I had not heard previously and which seems too theoretical [from Paulo’s comments] to explain why this rule would be the sole one. As I kept looking for Čencov’s references on the Web, I found Nick Polson’s thesis and the above quote. So maybe Nick could tell us more!

However, my uncertainty about the uniqueness of Jeffreys’ rule stems from the fact that, f I decide on a favourite or reference parametrisation—as Jeffreys indirectly does when selecting the parametrisation associated with a constant Fisher information—and on a prior derivation from the sampling distribution for this parametrisation, I have derived a parametrisation invariant principle. Possibly silly and uninteresting from a Bayesian viewpoint but nonetheless invariant.