Archive for Philadelphia

uniform correlation mixtures

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on December 4, 2015 by xi'an

Philadelphia, Nov. 01, 2010Kai Zhang and my friends from Wharton, Larry Brown, Ed George and Linda Zhao arXived last week a neat mathematical foray into the properties of a marginal bivariate Gaussian density once the correlation ρ is integrated out. While the univariate marginals remain Gaussian (unsurprising, since these marginals do not depend on ρ in the first place), the joint density has the surprising property of being

[1-Φ(max{|x|,|y|})]/2

which turns an infinitely regular density into a density that is not even differentiable everywhere. And which is constant on squares rather than circles or ellipses. This is somewhat paradoxical in that the intuition (at least my intuition!) is that integration increases regularity… I also like the characterisation of the distributions factorising through the infinite norm as scale mixtures of the infinite norm equivalent of normal distributions. The paper proposes several threads for some extensions of this most surprising result. Other come to mind:

  1. What happens when the Jeffreys prior is used in place of the uniform? Or Haldane‘s prior?
  2. Given the mixture representation of t distributions, is there an equivalent for t distributions?
  3. Is there any connection with the equally surprising resolution of the Drton conjecture by Natesh Pillai and Xiao-Li Meng?
  4. In the Khintchine representation, correlated normal variates are created by multiplying a single χ²(3) variate by a vector of uniforms on (-1,1). What are the resulting variates for other degrees of freedomk in the χ²(k) variate?
  5. I also wonder at a connection between this Khintchine representation and the Box-Müller algorithm, as in this earlier X validated question that I turned into an exam problem.

Art brut

Posted in pictures, Travel with tags , on January 29, 2011 by xi'an

Art brut

Posted in pictures with tags , on December 26, 2010 by xi'an

Disas-tea-R at dawn

Posted in Linux, R, Travel with tags , , , , , , , , on December 17, 2010 by xi'an

This was bound to happen sooner or later, given my addiction to tea and sleepless nights, so I eventually managed to spill a cup of tea over my Mac… I had been working for a few hours in my hotel room in Philadelphia, completing an ABC paper with Jean-Michel Marin and Robin Ryder. We had been running experiments in R with Jean-Michel over the past days and I wanted to check some details with him about some graphs he sent me, so we got into a Skype conversation. At the same time, I was running an alternative R code to compare with his, and starting a new ‘Og entry about a current campaign against road accidents. And drinking my fifth or sixth cuppa of the morning. I suddenly realised dawn had come and stood up to raise the blinds next to my desk. Completely forgetting about the earphones on my head. The obvious then occurred: the earphone cord stretched, pulling the teacup over and I turned back to see the keyboard covered with tea… Disaster! I tipped the computer over and grabbed the hotel hairdryer to try to dry it as quickly as possible (apologies to the next room neighbour!). Contrary to all advices, I did not turn the Mac off but kept running the R program instead to add to the heat of the dryer. In retrospect this was quite silly and I am lucky to get out with only two keys not working!

Smooth plane ride

Posted in Travel with tags , , on December 15, 2010 by xi'an

The Delta flight from Paris to Philadelphia was a mix of new and old, of highs and downs, with an exit seat (doubly exit in that I was first out of the plane and through custom!), a plug for my computer and free wireless connection (a first!), and, on the down side, an old-fashioned plane and crew, terrible food, worst-ever tea that tasted like dish-washing water and a flight attendant wishing us “enjoy!” each time she was pouring water… Since we arrived one hour earlier and I reached my hotel next to Wharton before the scheduled landing time, I should not complain, however..

Back to Philly

Posted in Statistics, Travel, University life with tags , , , , , , , on December 15, 2010 by xi'an

Today and tomorrow, I am attending a conference in Wharton in honour of Larry Brown for his 70th birthday. I met Larry in 1988 when visiting Cornell for the year—even using his office in the Math department while he was away on a sabbatical leave—and it really does not feel like that long ago, nor does it feel like Larry is any close to 70 as he looks essentially the same as 22 years ago! The conference is reflecting Larry’s broad range of research from decision-theory and nonparametrics to data analysis. I am thus very glad to celebrate Larry’s birthday with a whole crowd of old and more recent friends. (My talk on Rao-Blackwellisation will be quite similar to the seminar I gave in Stanford last summer [except that I have to talk twice as fast!])

Weird jetlag

Posted in pictures, Travel with tags , , on November 14, 2010 by xi'an

While in Philadelphia, I tried to keep on French time (to avoid jetlag on my way back) by waking up between 2am and 3am every morning. This worked out quite well (and gave me an additional window for efficient study!). However, since I am back, I have been faced with the weird phenomenon that I wake up at 2:40am every morning and cannot go back to sleep! This is quite annoying and had never occurred previously. Maybe my brain got somehow so wired to this “emergency wake-up call” before 3 that it needs time to erase it!

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