Archive for tramways

Tramway du Mont Blanc [jatp]

Posted in Statistics with tags , , , , , , , , , , , , on March 27, 2022 by xi'an

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..!)

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