Archive for Ganges
IISA 2026 in Varanasi [26-29 Dec]
Posted in pictures, Travel, University life with tags annual conference, Banaras Hindu University, Bénarés, BHU, Ganges, IISA, IISA 2026, India, International Indian Statistical Association, Uttar Pradesh, Varanasi, Western Ghats on March 22, 2026 by xi'an
Fisher’s lost information
Posted in Books, Kids, pictures, Statistics, Travel with tags asymptotic variance, central limit theorem, Fisher information, Fréchet-Darmois-Cramèr-Rao bound, Ganges, jatp, uniform distribution, Varanasi on February 11, 2019 by xi'an
After a post on X validated and a good discussion at work, I came to the conclusion [after many years of sweeping the puzzle under the carpet] that the (a?) Fisher information obtained for the Uniform distribution U(0,θ) as θ⁻¹ is meaningless. Indeed, there are many arguments:
- The lack of derivability of the indicator function for x=θ is a non-issue since the derivative is defined almost everywhere.
- In many textbooks, the Fisher information θ⁻² is derived from the Fréchet-Darmois-Cramèr-Rao inequality, which does not apply for the Uniform U(0,θ) distribution.
- One connected argument for the expression of the Fisher information as the expectation of the squared score is that it is the variance of the score, since its expectation is zero. Except that it is not zero for the Uniform U(0,θ) distribution.
- For the same reason, the opposite of the second derivative of the log-likelihood is not equal to the expectation of the squared score. It is actually -θ⁻²!
- Looking at the Taylor expansion justification of the (observed) Fisher information, expanding the log-likelihood around the maximum likelihood estimator does not work since the maximum likelihood estimator does not cancel the score.
- When computing the Fisher information for an n-sample rather than a 1-sample, the information is n²θ⁻², rather than nθ⁻².
- Since the speed of convergence of the maximum likelihood estimator is of order n⁻², the central limit theorem does not apply and the limiting variance of the maximum likelihood estimator is not the Fisher information.
Varanasi unholy air
Posted in pictures, Travel with tags air pollution, air quality, cremation, Ganges, Gwalior Fort, India, micro-particle, Northern India, pyre, Rajasthan, Varanasi on December 15, 2016 by xi'an
One of my lasting memories of my trip to Varanasi four years ago is the poor quality of the air, with an almost constant fog over the city, fed by open air fires everywhere and aggressive vehicle exhaust, rather than by the few cremation pyres by the Ganges… I read today in The Guardian that the city actually ranks worst in India for its air quality. (I also read in that article that Gwalior had similar issues, although I remember a pleasant walk around the fort there, in the sun. Presumably on one of the few “good” air quality days.) Not that Paris is doing great in the past days, with a whole week of ineffective driving restrictions that left wood heating operating at full blast. I did not feel the air difference while biking, but I presume the impact of the micro-particles central to those pollution alerts is more long-term!
India snapshot (#21)
Posted in Statistics with tags boats, flowers, Ganges, India, sunset, Uttar Pradesh, Varanasi, votive candles on January 12, 2013 by xi'an
We went before sunset on a boat ride along the Ganges, terminating in the main ghat,Dashashwamedh Ghat (दशाश्वमेध घाट), in a pleasant temperature announcing the return of warmer weather. As we were slowly drifting with the motor off, some passengers released a marigold bowl with a lit candle in the midst…
India snapshot (#20)
Posted in pictures, Travel with tags cow, Ganges, India, Uttar Pradesh, Varanasi on January 12, 2013 by xi'an
Last step of the Indian trip, in Varanasi, when walking the ghats, with a local. And the Ganges as a background.
