Archive for All the pretty horses

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 Border trilogy

Posted in Books with tags , , , , on December 18, 2010 by xi'an

The Border trilogy is made of three books written by Cormac McCarthy: All the pretty horses, The crossing, and Cities of the plain. I have now finished reading those books and I am quite impressed by the dark beauty of the stories as well as by the unusual style of the writer. (I first wanted to read The Road and then decided on trying an earlier book of McCarthy.) Those books are “classics” in the sense that they refer to both a universe and a way to telling stories that have now vanished. (This feeling of reading a “classic” is of course amplified by my version of Border trilogy published in Everyman’s Library collection!) Cormac McCarthy is sometimes compared with William Faulkner; while I cannot really judge whether or not the comparison is apt, there is indeed something of Faulkner’s in the Biblical quality of McCarthy’s stories. Indeed, when I started All the pretty horses, I thought this was a realist story set in a past Southwest about cowboys but the novel soon turned into an allegorical tale about doomed love and lost innocence. This is even stronger in The crossing where each encounter of the brothers with strangers has a  tale-within-the-tale picaresque quality, most of the characters launching into stories  that sound like parables from an alternate Bible. Dialogues abound in the books but they rarely feel like chatter. (Having to decipher half of them from Spanish does add weight to this point!) Mexico is depicted like a primeval and a-moral Eden, where strangers are fed with no question asked, caballeros are considered as an aristocracy, and law-and-order does not mean anything, the local police summarily executing a major character in All the pretty horses… But the morbid fascination it exerts on the young cowboys is so strong it only fits within the Biblical message of the novels, what the New Yorker calls the “deterministic mythmaking of McCarthy”. Although not an easy read, I certainly enjoyed The crossing the most, because of its otherworldliness, the main character Billy pursuing his quests against all odds, first for a wolf,  then for horses and lastly for his brother. The final scene with the mangled dog is a desperately sad counterpoint to the starting plot with the wolf… The last piece of the trilogy Cities of the plain does not ring so true because of the different attitude of this same character. Again, this is the discovery of a major writer for me and I will certainly read some more books of his in a near future!