## in the bus [jatp]

Posted in pictures, Travel with tags , , , , , , , on January 13, 2018 by xi'an

## morning devotions at Dakshineswar [jatp]

Posted in Statistics with tags , , , , , , , , on January 5, 2018 by xi'an

## Better together in Kolkata [slides]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on January 4, 2018 by xi'an

Here are the slides of the talk on modularisation I am giving today at the PC Mahalanobis 125 Conference in Kolkata, mostly borrowed from Pierre’s talk at O’Bayes 2018 last month:

[which made me realise Slideshare has discontinued the option to update one’s presentation, forcing users to create a new presentation for each update!] Incidentally, the amphitheatre at ISI is located right on top of a geological exhibit room with a reconstituted Barapasaurus tagorei so I will figuratively ride a dinosaur during my talk!

## Mahalanobis at the bus-stop [jatp]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , on January 3, 2018 by xi'an

Two bus-stops around the Indian Statistical Institute, featuring its founder, Prasanta Chandra Mahalanobis.

## back to Kolkata [শুভ নব বর্ষ]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , on January 1, 2018 by xi'an

With high probability (!), I am off to Kolkata tonight, almost an exact year after I visited the city and the Department of Statistics of the University of Kolkata. On this occasion, I will attend a conference celebrating the 125th birthday of Mahalanobis and be staying at the Indian Statistical Institute, in another part of the city. Although I will only stay there for three days, I am looking forward meeting old friends and new faces, enjoying Bengali food and replenishing my reserves of Darjeeling tea. Shubho Nabobarsho (Happy New Year in Bengali)! As in the previous trip, I was also invited at a second conference at the Indian Association For Productivity, Quality & Reliability, on New Paradigms in Statistics for Scientific and Industrial Research, but decided against talking there for fear of being stuck for hours in the infamous Kolkata traffic.

## Jayanta Kumar Ghosh [1937-2017]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , on October 2, 2017 by xi'an

Just head from Sonia and Judith that our friend and fellow Bayesian Jayanta K Ghosh (জয়ন্ত কুমার ঘোষ in Bengali) has passed away a few days ago in Lafayette. He was a wonderful man, very kind to everyone and open for discussing all aspects of Bayesian theory and methodology. While he worked on many branches of statistics, he is more know to Bayesians for his contributions to Bayesian asymptotics. From Bernstein-von-Mises convergence theorems to frequentist validation of non-informative priors, to the Bayesian analysis of infinite dimensional problems, including consistency of posteriors and rates of convergence, and to Bayesian and Empirical Bayes model selection rules in high dimensional problems. He also wrote an introductory textbook on Bayesian Statistics ten years ago with Mohan Delampady and Tapas Samanta. And a monograph of higher order asymptotics. I knew from this summer that J K was quite sick and am quite sad to learn of his demise. He will be missed by all for his gentleness and by Bayesians for his contributions to the fields of objective and non-parametric Bayesian statistics…

## 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!)