## snapshot from Oxford [jatp]

Posted in pictures, Travel with tags , , , , , , , , on April 21, 2018 by xi'an

## fiducial simulation

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on April 19, 2018 by xi'an

While reading Confidence, Likelihood, Probability), by Tore Schweder and Nils Hjort, in the train from Oxford to Warwick, I came upon this unexpected property shown by Lindqvist and Taraldsen (Biometrika, 2005) that to simulate a sample y conditional on the realisation of a sufficient statistic, T(y)=t⁰, it is sufficient (!!!) to simulate the components of  y as y=G(u,θ), with u a random variable with fixed distribution, e.g., a U(0,1), and to solve in θ the fixed point equation T(y)=t⁰. Assuming there exists a single solution. Brilliant (like an aurora borealis)! To borrow a simple example from the authors, take an exponential sample to be simulated given the sum statistics. As it is well-known, the conditional distribution is then a (rescaled) Beta and the proposed algorithm ends up being a standard Beta generator. For the method to work in general, T(y) must factorise through a function of the u’s, a so-called pivotal condition which brings us back to my post title. If this condition does not hold, the authors once again brilliantly introduce a pseudo-prior distribution on the parameter θ to make it independent from the u’s conditional on T(y)=t⁰. And discuss the choice of the Jeffreys prior as optimal in this setting even when this prior is improper. While the setting is necessarily one of exponential families and of sufficient conditioning statistics, I find it amazing that this property is not more well-known [at least by me!]. And wonder if there is an equivalent outside exponential families, for instance for simulating a t sample conditional on the average of this sample.

## A discovery of wromynce

Posted in Books, Travel, University life with tags , , , on March 4, 2018 by xi'an

While recovering from this minor food poisoning bout in Oxford the other week, I took a break by having an early night after my class and reading a book hurriedly purchase from a local bookstore, A Discovery of Witches, by Deborah Harkness, which title sounded (wrongly) familiar, and which turned out to be a soapy wromynce (my own mix of witch, vampyre, and romance…) involving a reluctant witch and a very ancient vampyre falling in love against the eternal rules of their respective communities. Including all imaginable clichés on these creatures, like enormous wealth, superior intelligence, involvement into human history, science, arts, politics, &tc., since the dawn of time (at the very least). The style is appalling, with one dimensional characters and less-than-one-dimension plots, a hotchpotch of alchemy and the most advanced science, of historical facts and of the most threadbare conspiracy theories, the main character oscillating between the rational, precocious, sport-obsessed, Oxford academic and a Harlequin-like damsel-in-distress having lost her intellectual pursuits… As in La Belle Sauvage, the book has a strong connection with Oxford and its colleges at the beginning of the book that may make for an extra incentive, but it was a relief to abandon the unfinished book there before returning to Paris|

## la belle sauvage [book review]

Posted in Statistics with tags , , , , , , , , , , , , , , , on February 25, 2018 by xi'an

Another book I brought back from Austin. And another deeply enjoyable one, although not the end of a trilogy of trilogies this time. This book, La Belle Sauvage, is first in a new trilogy by Philip Pullman that goes back to the early infancy of the hero of His Dark Materials, Lyra. Later volumes will take place after the first trilogy.

This is very much a novel about Oxford, to the point it sometimes seems written only for people with an Oxonian connection. After all, the author is living in Oxford… (Having the boat of the two characters passing by the [unnamed] department of Statistics at St. Giles carried away by the flood was a special sentence for me!)

Also, in continuation of His Dark Materials, a great steampunk universe, with a very oppressive Church and so far a limited used of magicks! Limited to the daemons, again in continuation with past volumes…

Now, some passages of the book remind me of Ishiguro’s buried giant, in the sense that the characters meeting myths from other stories may “really” meet them or instead dream. This is for instance the case when they accost at a property where an outworldy party is taking place and no-one is noticing them. Or when they meet a true giant that is a river deity, albeit not in the spirit of Ben Aaronovitch’s Rivers of London novels.

The story is written in the time honoured setup of teenager discovery travels, with not so much to discover as the whole country is covered by water. And the travel gets a wee bit boring after a while, with a wee bit too many coincidences, the inexplicable death (?) of a villain, and an hurried finale, where the reverse trip of the main characters takes a page rather than one book…

Trivia: La Belle Sauvage was also the name of the pub in Ludgate Hill where Pocahontas and her brother Tomocomo stayed when they first arrived in London. And The Trout is a true local pub, on the other side of Port Meadow [although I never managed to run that far in that direction while staying in St. Hugh, Oxford, last time, the meadow being flooded!].

Looking forward the second volume (already written, so no risk of The Name of the Wind or Game of Thrones quagmires, i.e., an endless wait for the next volume!), hoping the author keeps up the good work, the right tension in the story, and avoids by all means parallel universes, which were so annoying in the first trilogy! (I do remember loosing interest in the story during the second book and having trouble finishing the third one. I am not sure my son [who started before me] ever completed the trilogy…)

## amazing appendix

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , on February 13, 2018 by xi'an

In the first appendix of the 1995 Statistical Science paper of Besag, Green, Higdon and Mengersen, on MCMC, “Bayesian Computation and Stochastic Systems”, stands a fairly neat result I was not aware of (and which Arnaud Doucet, with his unrivalled knowledge of the literature!, pointed out to me in Oxford, avoiding me the tedium to try to prove it afresco!). I remember well reading a version of the paper in Fort Collins, Colorado, in 1993 (I think!) but nothing about this result.

It goes as follows: when running a Metropolis-within-Gibbs sampler for component x¹ of a collection of variates x¹,x²,…, thus aiming at simulating from the full conditional of x¹ given x⁻¹ by making a proposal q(x|x¹,x⁻¹), it is perfectly acceptable to use a proposal that depends on a parameter α (no surprise so far!) and to generate this parameter α anew at each iteration (still unsurprising as α can be taken as an auxiliary variable) and to have the distribution of this parameter α depending on the other variates x²,…, i.e., x⁻¹. This is the surprising part, as adding α as an auxiliary variable was messing up the update of x⁻¹. But the proof as found in the 1995 paper [page 35] does not require to consider α as such as it establishes global balance directly. (Or maybe still detailed balance when writing the whole Gibbs sampler as a cycle of Metropolis steps.) Terrific! And a whiff mysterious..!

## annual visit to Oxford

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , on February 1, 2018 by xi'an

As in every year since 2014, I am spending a few days in Oxford to teach a module on Bayesian Statistics to our Oxford-Warwick PhD students. This time I was a wee bit under the weather due to a mild case of food poisoning and I can only hope that my more than sedate delivery did not turn definitely the students away from Bayesian pursuits!

The above picture is at St. Hugh’s College, where I was staying. Or should it be Saint Hughes, since this 12th century bishop was a pre-Brexit European worker from Avalon, France… (This college was created in 1886 for young women of poorer background. And only opened to male students a century later. The 1924 rules posted in one corridor show how these women were considered to be so “dangerous” by the institution that they had to be kept segregated from men, except their brothers!, at all times…)