Archive for tramways

from tramway to Panzer (or back!)…

Posted in Books, pictures, Statistics with tags , , , , , , on June 14, 2019 by xi'an

Although it is usually presented as the tramway problem, namely estimating the number of tram or bus lines in a city given observing one line number, including The Bayesian Choice by yours truly, the original version of the problem is about German tanks, Panzer V tanks to be precise, which total number M was to be estimated by the Allies from their observation of serial numbers of a number k of tanks. The Riddler is restating the problem when the only available information is made of the smallest, 22, and largest, 144, numbers, with no information about the number k itself. I am unsure what the Riddler means by “best” estimate, but a posterior distribution on M (and k) can be certainly be constructed for a prior like 1/k x 1/M² on (k,M). (Using M² to make sure the posterior mean does exist.) The joint distribution of the order statistics is

\frac{k!}{(k-2)!} M^{-k} (144-22)^{k-2}\, \Bbb I_{2\le k\le M\ge 144}

which makes the computation of the posterior distribution rather straightforward. Here is the posterior surface (with an unfortunate rendering of an artefactual horizontal line at 237!), showing a concentration near the lower bound M=144. The posterior mode is actually achieved for M=144 and k=7, while the posterior means are (rounded as) M=169 and k=9.

Brussels snapshot #3 [jatp]

Posted in pictures, Running, Travel with tags , , , , on June 23, 2018 by xi'an

ABC gas

Posted in pictures, Running, Travel with tags , , , , , , , on August 9, 2017 by xi'an

Self-Transcendence 2 mile races in Helsinki

Posted in Running, Travel, University life with tags , , , , , , , , , , , on July 26, 2017 by xi'an

Upon our arrival in Helsinki for EMS 2017, Jean-Michel Marin pointed out to me the existence of a 2 miles race the next day [as every Tuesday], indicated on the webpage of the conference. And encouraged me to run it. As I had brought my running gear and did not need preparation for a 2 miles [a mere loop in the parc!], I decided to try the race and we took a tram all the way to a faraway suburb where a few other runners had gathered. It was very relaxed and friendly, with recyclable cloth bibs and free juice available. Against all odds, I managed to win the race, with a first mile under six minutes thanks to another runner rushing me. And got a tee shirt as a reward. (Checking on Wikipedia later, I found that Sri Chinmoy was an Indian guru advocating running as a form of meditation, which I find rather absurd as I am anything but meditating when running a race..!)

snowed-in Paris

Posted in pictures with tags , , , , , , , , on March 17, 2013 by xi'an

Fontaine des Innocents, Paris, March 12, 2013Just like my astronomy colleague from Brighton, I do wonder why so little snow on the ground creates so much havoc on the transportation network. RER trains have been crawling at a snail-like pace, buses cancelled and trams inoperative for the past few days. I presume this is because there is no degree of freedom left in the way those public transportation systems are operated. They are bursting at every possible seam for lack of sufficient investment in material and people, and, as a result, cannot handle any event that would require any extra manpower (like running the trains all night long to keep the rails free from snow and ice…) The electricity company EDF has started relying on its (young) retirees in cases of major crises and I think the rail companies should do the same.

Melbourne trams

Posted in pictures, Travel with tags , , on August 3, 2012 by xi'an

(Melbourne has one of the largest tram networks in the World, some specimens below.)