## Archive for Himalayas

## first 8000

Posted in Mountains with tags 8000's, Annapurna, Annapurna Premier 8000, Carnets de Vertige, climbing, Gaston Rebuffat, Himalayas, La Piste des Cimes, Les conquérants de l'inutile, Lionel Terray, Louis Lachenal, Maurice Herzog, Nepal, sherpas on June 3, 2020 by xi'an## Ueli Steck dies on Nupse [Ueli Steck tödlich verunglückt]

Posted in Books, Mountains, Running with tags Bernese Alps, Eiger, Everest, Himalayas, mountaineering, Nupse, Switzerland, Ueli Steck on April 30, 2017 by xi'an**U**eli Steck was a Swiss climber renowned for breaking speed records on the hardest routes of the Alps. Including the legendary Eigerwand. And having been evacuated under death threats from the Everest base camp two years ago. I have been following on Instagram his preparation for another speed attempt at Everest the past weeks and it is a hug shock to learn he fell to his death on Nupse yesterday. Total respect to this immense Extrembergsteiger, who has now joined the sad cenacle of top climbers who did not make it back…

## optimal Bernoulli factory

Posted in Statistics with tags Bernoulli factory, Cramer-Rao lower bound, Darjeeling, Debabrata Basu, Himalayas, India, Kangchenjunga, Kolkata, Lovàsz, Mark Huber, University of Calcutta on January 17, 2017 by xi'an**O**ne of the last arXivals of the year was this paper by Luis Mendo on an optimal algorithm for Bernoulli factory (or Lovàsz‘s or yet Basu‘s) problems, i.e., for producing an unbiased estimate of f(p), 0<p<1, from an unrestricted number of Bernoulli trials with probability *p* of heads. (See, e.g., Mark Huber’s recent book for background.) This paper drove me to read an older 1999 unpublished document by Wästlund, unpublished because of the overlap with Keane and O’Brien (1994). One interesting gem in this document is that Wästlund produces a Bernoulli factory for the function *f(p)=√p*, which is not of considerable interest *per se*, but which was proposed to me as a puzzle by Professor Sinha during my visit to the Department of Statistics at the University of Calcutta. Based on his 1979 paper with P.K. Banerjee. The algorithm is based on a stopping rule N: throw a fair coin until the number of heads n+1 is greater than the number of tails n. The event N=2n+1 occurs with probability

[Using a biased coin with probability *p* to simulate a fair coin is straightforward.] Then flip the original coin n+1 times and produce a result of 1 if at least one toss gives heads. This happens with probability *√p*.

Mendo generalises Wästlund‘s algorithm to functions expressed as a power series in *(1-p)*

with the sum of the weights being equal to one. This means proceeding through Bernoulli B(p) generations until one realisation is one or a probability

event occurs [which can be derived from a Bernoulli B(p) sequence]. Furthermore, this version achieves asymptotic optimality in the number of tosses, thanks to a form of Cramer-Rao lower bound. (Which makes yet another connection with Kolkata!)