## Ueli Steck dies on Nupse [Ueli Steck tödlich verunglückt]

Posted in Books, Mountains, Running with tags , , , , , , , on April 30, 2017 by xi'an

Ueli 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 , , , , , , , , , , on January 17, 2017 by xi'an

One 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 This paper drove me to read an older 1999 unpublished document by Wästlund, unpublished because of the overlap with Keane and O’Brien (1994).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

${2n \choose n} \big/ 2^{2n+1}$

[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)

$f(p)=1-\sum_{i=1}^\infty c_i(1-p)^i$

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

$c_i\big/1-\sum_{j=1}^{i-1}c_j$

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!)

## कञ्चनजङ्घा [jatp]

Posted in Statistics with tags , , , , , , , , , , , on January 1, 2017 by xi'an

## कञ्चनजङ्घा [jatp]

Posted in Mountains, pictures, Travel with tags , , , , , , , , on December 27, 2016 by xi'an

## বড়দিনের শুভেচ্ছা

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , on December 25, 2016 by xi'an

বড়দিনের শুভেচ্ছা

கிறிஸ்துமஸ் வாழ்த்துக்கள்

क्रिसमस की बधाई

క్రిస్మస్ శుభాకాంక్షలు

ਕ੍ਰਿਸਮਸ ਸਲਾਮ

ક્રિસમસ શુભેચ્છાઓ

ക്രിസ്മസ് ആശംസകൾ

## Himalayas [jatp]

Posted in Statistics with tags , , , , on December 19, 2016 by xi'an

## off to India

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on December 18, 2016 by xi'an

I am off to India today to take part in the celebration of the Platinum Jubilee of the Department of Statistics of the University of Calcutta, which was created in 1941 by Prasanta Chandra Mahalanobis. (One of the first cohort of students to complete their studies in this department was C.R. Rao.) The conference is organised by Asis Kumar Chattopadhyay whom I first met in Bangalore a few years ago and who visited Frédéric Arenou and myself last summer. This trip is quite exciting, from visiting this department to discovering Calcutta and Western Bengal, with a short stop in Darjeeling and the Himalayas foothills on the way there… Obviously, ‘Og mileage may vary in the coming days, depending on the wireless coverage. (But expect mostly pictures, anyway!)