Archive for Gösta Mittag-Leffler

inverse stable priors

Posted in Statistics with tags , , , , , , on November 24, 2017 by xi'an

Dexter Cahoy and Joseph Sedransk just arXived a paper on so-called inverse stable priors. The starting point is the supposed defficiency of Gamma conjugate priors, which have explosive behaviour near zero. Albeit remaining proper. (This behaviour eventually vanishes for a large enough sample size.) The alternative involves a transform of alpha-stable random variables, with the consequence that the density of this alternative prior does not have a closed form. Neither does the posterior. When the likelihood can be written as exp(a.θ+b.log θ), modulo a reparameterisation, which covers a wide range of distributions, the posterior can be written in terms of the inverse stable density and of another (intractable) function called the generalized Mittag-Leffler function. (Which connects this post to an earlier post on Sofia Kovaleskaya.) For simulating this posterior, the authors suggest using an accept-reject algorithm based on the prior as proposal, which has the advantage of removing the intractable inverse stable density but the disadvantage of… simulating from the prior! (No mention is made of the acceptance rate.) I am thus reserved as to how appealing this new proposal is, despite “the inverse stable density (…) becoming increasingly popular in several areas of study”. And hence do not foresee a bright future for this class of prior…

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.