Archive for Varanasi

mostly nuisance, little interest

Posted in Statistics, University life with tags , , , , , , on February 7, 2013 by xi'an

tree next to my bike parking garage at INSEE, Malakoff, Feb. 02, 2012Sorry for the misleading if catchy (?) title, I mean mostly nuisance parameters, very few parameters of interest! This morning I attended a talk by Eric Lesage from CREST-ENSAI on non-responses in surveys and their modelling through instrumental variables. The weighting formula used to compensate for the missing values was exactly the one at the core of the Robins-Wasserman paradox, discussed a few weeks ago by Jamie in Varanasi. Namely the one with the estimated probability of response at the denominator: The solution adopted in the talk was obviously different, with linear estimators used at most steps to evaluate the bias of the procedure (since researchers in survey sampling seem particularly obsessed with bias!)

On a somehow related topic, Aris Spanos arXived a short note (that I read yesterday) about the Neyman-Scott paradox. The problem is similar to the Robins-Wasserman paradox in that there is an infinity of nuisance parameters (the means of the successive pairs of observations) and that a convergent estimator of the parameter of interest, namely the variance common to all observations, is available. While there exist Bayesian solutions to this problem (see, e.g., this paper by Brunero Liseo), they require some preliminary steps to bypass the difficulty of this infinite number of parameters and, in this respect, are involving ad-hocquery to some extent, because the prior is then designed purposefully so. In other words, missing the direct solution based on the difference of the pairs is a wee frustrating, even though this statistic is not sufficient! The above paper by Brunero also my favourite example in this area: when considering a normal mean in large dimension, if the parameter of interest is the squared norm of this mean, the MLE ||x||² (and the Bayes estimator associated with Jeffreys’ prior) is (are) very poor: the bias is constant and of the order of the dimension of the mean, p. On the other hand, if one starts from ||x||² as the observation (definitely in-sufficient!), the resulting MLE (and the Bayes estimator associated with Jeffreys’ prior) has (have) much nicer properties. (I mentioned this example in my review of Chang’s book as it is paradoxical, gaining in efficiency by throwing away “information”! Of course, the part we throw away does not contain true information about the norm, but the likelihood does not factorise and hence the Bayesian answers differ…)

I showed the paper to Andrew Gelman and here are his comments:

Spanos writes, “The answer is surprisingly straightforward.” I would change that to, “The answer is unsurprisingly straightforward.” He should’ve just asked me the answer first rather than wasting his time writing a paper!

The way it works is as follows. In Bayesian inference, everything unknown is unknown, they have a joint prior and a joint posterior distribution. In frequentist inference, each unknowns quantity is either a parameter or a predictive quantity. Parameters do not have probability distributions (hence the discomfort that frequentists have with notation such as N(y|m,s); they prefer something like N(y;m,s) or f_N(y;m,s)), while predictions do have probability distributions. In frequentist statistics, you estimate parameters and you predict predictors. In this world, estimation and prediction are different. Estimates are evaluated conditional on the parameter. Predictions are evaluated conditional on model parameters but unconditional on the predictive quantities. Hence, mle can work well in many high-dimensional problems, as long as you consider many of the uncertain quantities as predictive. (But mle is still not perfect because of the problem of boundary estimates, e.g., here..

R finals

Posted in R, Statistics, University life with tags , , , , , , , , on January 31, 2013 by xi'an

From my office in Dauphine, on the hottest day of the year (so far)...On the morning I returned from Varanasi and the ISBA meeting there, I had to give my R final exam (along with three of my colleagues in Paris-Dauphine). This year, the R course was completely in English, exam included, which means I can post it here as it may attract more interest than the French examens of past years…

I just completed grading my 32 copies, all from exam A, which takes a while as I have to check (and sometimes recover) the R code, and often to correct the obvious mistakes to see if the deeper understanding of the concepts is there. This year student cohort is surprisingly homogeneous: I did not spot any of the horrors I may have mentioned in previous posts.

I must alas acknowledge a grievous typo in the version of Exam B that was used the day of the final: cutting-and-pasting from A to B, I forgot to change the parameters in Exercise 2, asking them to simulate a Gamma(0,1). It is only after half an hour that a bright student pointed out the impossibility… We had tested the exams prior to printing them but this somehow escaped the four of us!

Now, as I was entering my grades into the global spreadsheet, I noticed a perfect… lack of correlation between those and the grades at the midterm exam. I wonder what that means: I could be grading at random, the levels in November and in January could be uncorrelated, some students could have cheated in November and others in January, student’s names or file names got mixed up, …? A rather surprising outcome!

grades of some of my students at the midterm and finals R exams

brands with a tree logo…

Posted in Mountains, Travel with tags , , , , , , , , , on January 20, 2013 by xi'an

As the cold wave in Varanasi caught me by surprise, I asked the conference organisers for a place to buy a down jacket and they kindly drove me to a nice store called Woodland within the city. I purchased a cheap down-like jacket there (as demonstrated by the newspaper excerpt!) that solved my problem. And I thus discovered a brand that looked surprisingly similar to Timberland, slowly coming to realise this was the whole point: change Timber into Wood, slightly modify the tree in the logo, and you get a local brand that recycles Timberland designs and products to their own profit… (This seems to be a common occurrence in India, judging from this New York Times article.) Anyway, it is rather entertaining to visit the Woodland website, as they mimic major outdoor brand websites like Patagonia or Petzl, but do not offer any material one could seriously consider taking hiking and even less climbing! (Besides the jacket that managed to keep me warm for the rest of the meeting!, I also bought a cheap pair of sneakers and that quickly  proved to be a mistake, as the fit is only approximate and the material of poor quality.)

Mother India

Posted in pictures, Travel with tags , , , , on January 15, 2013 by xi'an

advertising in the streets of Varanasi, Uttar Pradesh, Jan. 10, 2013I saw several Amul posters during my trip to India and they all were related to women’s rights in the aftermath of the atrocious rape in Delhi, so I assumed this was a political party or organisation. However, when checking on the Web, I found that Amul is a dairy cooperative from the State of Gujarat, selling milk and milk products like ghee. It however runs ads involving their mascot, which can be quite political. Like the one above taken on my way to the airport in Varanasi. Or the one protesting the repression of the post-rape demonstrations in Delhi.

breaking news…

Posted in Statistics with tags , , , , on January 14, 2013 by xi'an

article in local Hindi newpaper about the conference, Varanasi airport, Jan. 10, 2013A newspapers excerpt I glimpsed at the conference and copied at the airport. I cannot tell much about the contents, not even spot my name!, by fellow travellers told me it focussed on the application part of the conference, mentioning leeches in the title… Fun, anyway, if you do not mind the orange down coat!

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