## chance meeting

Posted in Statistics with tags , , , , , , , , , on July 10, 2018 by xi'an

As I was travelling to Coventry yesterday, I spotted this fellow passenger on the train from Birmingham with a Valencia 9 bag, and a chat with him. It was a pure chance encounter as he was not attending our summer school, but continued down the line. (These bags are quite sturdy and I kept mine until a zipper broke.)

## Байкало-Амурская магистраль/БАМ

Posted in Statistics with tags , , , , , , , , , on April 15, 2018 by xi'an

While in Chamonix last month I dropped by the Guérin editions bookstore, always full of tantalising books on climbing and mountaineering, travelling and travellers. I managed to escape with only two small books, one on a young climber stuck for 100 hours at the top of Aiguilles Vertes [not far from my last ice-climb!] and the other one a railway trip along the Baïkal-Amour Mainline (BAM), which goes from the Baïkal Lake to Sovietskaïa Gavan, north of the Trans-Siberian line. The book is not the ultimate travel book as most of the pages are about historical features surrounding this line, first and foremost the constant reminder that Gulag prisoners were relentlessly exploited to build this line, which follows a macabre route along Siberian camps. The trip finishes not at the end of the BAM line or in Vladivostok, but on Sakhaline Island, which was a penitential colony from the mid-1800’s, as covered by Anton Tchekov in a statistical study and a short story, The Murder… (Comments about characters crossed throughout the trip are rarely to the benefit of these characters.) While I do not make this travel book or the places it crosses sound particularly exciting, it still carries with it the inducing whiff of faraway places, which makes me wish I could see Lake Baïkal or Vladivostok one day in the future, if not travel the entire line. And it also brought back memories of Corto Maltese in Siberia, which remains one of my favourites…

## self-portrait on a railway board [jatp]

Posted in Kids, Mountains, pictures, Travel with tags , , , , , , on December 31, 2017 by xi'an

## an elegant result on exponential spacings

Posted in Statistics with tags , , , , , , , , , , , , , on April 19, 2017 by xi'an

A question on X validated I spotted in the train back from Lyon got me desperately seeking a reference in Devroye’s Generation Bible despite the abyssal wireless and a group of screeching urchins a few seats away from me… The question is about why

$\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$

when the Y’s are standard exponentials. Since this reminded me immediately of exponential spacings, thanks to our Devroye fan-club reading group in Warwick,  I tried to download Devroye’s Chapter V and managed after a few aborts (and a significant increase in decibels from the family corner). The result by Sukhatme (1937) is in plain sight as Theorem 2.3 and is quite elegant as it relies on the fact that

$\sum_{i=1}^n y_i=\sum_{j=1}^n (n-j+1)(y_{(j)}-y_{(j-1)})=\sum_{j=2}^n (y_{(j)}-y_{(1)})$

hence sums up as a mere linear change of variables! (Pandurang Vasudeo Sukhatme (1911–1997) was an Indian statistician who worked on human nutrition and got the Guy Medal of the RSS in 1963.)

## Statlearn17, Lyon

Posted in Kids, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , on April 6, 2017 by xi'an

Today and tomorrow, I am attending the Statlearn17 conference in Lyon, France. Which is a workshop with one-hour talks on statistics and machine learning. And which makes for the second workshop on machine learning in two weeks! Yesterday there were two tutorials in R, but I only took the train to Lyon this morning: it will be a pleasant opportunity to run tomorrow through a city I have not truly ever visited, if X’ed so many times driving to the Alps. Interestingly, the trip started in Paris with me sitting in the train next to another speaker at the conference, despite having switched seat and carriage with another passenger! Speaker whom I did not know beforehand and could only identify him by his running R codes at 300km/h.

## non-reversible Langevin samplers

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on February 6, 2017 by xi'an

In the train to Oxford yesterday night, I read through the recently arXived Duncan et al.’s Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation. Standing up the whole trip in the great tradition of British trains.

The paper is fairly theoretical and full of Foster-Lyapunov assumptions but aims at defending an approach based on a non-reversible diffusion. One idea is that the diffusion based on the drift {∇ log π(x) + γ(x)} is associated with the target π provided

∇ . {π(x)γ(x)} = 0

which holds for the Langevin diffusion when γ(x)=0, but produces a non-reversible process in the alternative. The Langevin choice γ(x)=0 happens to be the worst possible when considering the asymptotic variance. In practice however the diffusion need be discretised, which induces an approximation that may be catastrophic for convergence if not corrected, and a relapse into reversibility if corrected by Metropolis. The proposal in the paper is to use a Lie-Trotter splitting I had never heard of before to split between reversible [∇ log π(x)] and non-reversible [γ(x)] parts of the process. The deterministic part is chosen as γ(x)=∇ log π(x) [but then what is the point since this is Langevin?] or as the gradient of a power of π(x). Although I was mostly lost by that stage, the paper then considers the error induced by a numerical integrator related with this deterministic part, towards deriving asymptotic mean and variance for the splitting scheme. On the unit hypercube. Although the paper includes a numerical example for the warped normal target, I find it hard to visualise the implementation of this scheme. Having obviously not heeded Nicolas’ and James’ advice, the authors also analyse the Pima Indian dataset by a logistic regression!)

## Amtrak [jatp]

Posted in Kids, pictures, Travel with tags , , , , , on August 22, 2016 by xi'an