## latest math stats exam

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , , on January 28, 2023 by xi'an

As I finished grading our undergrad math stats exam (in Paris Dauphine) over the weekend, which was very straightforward this year, the more because most questions had already been asked on weekly quizzes or during practicals, some answers stroke me as atypical (but ChatGPT is not to blame!). For instance, in question 1, (c) received a fair share of wrong eliminations as g not being necessarily bounded. Rather than being contradicted by (b) being false. (ChatGPT managed to solve that question, except for the L² convergence!)

Question 2 was much less successful than we expected, most failures due to a catastrophic change of parameterisation for computing the mgf that could have been ignored given this is a Bernoulli model, right?! Although the students wasted quite a while computing the Fisher information for the Binomial distribution in Question 3… (ChatGPT managed to solve that question!)

Question 4 was intentionally confusing and while most (of those who dealt with the R questions) spotted the opposition between sample and distribution, hence picking (f), a few fell into the trap (d).

Question 7 was also surprisingly incompletely covered by a significant fraction of the students, as they missed the sufficiency in (c). (ChatGPT did not manage to solve that question, starting with the inverted statement that “a minimal sufficient statistic is a sufficient statistic that is not a function of any other sufficient statistic”…)

And Question 8 was rarely complete, even though many recalled Basu’s theorem for (a) [more rarely (d)] and flunked (c). A large chunk of them argued that the ancilarity of statistics in (a) and (d) made them [distributionally] independent of μ, therefore [probabilistically] of the empirical mean! (Again flunked by ChatGPT, confusing completeness and sufficiency.)

## deGPTed

Posted in Books, Kids, Statistics, University life with tags , , , , , on December 20, 2022 by xi'an

As shown above, automated chatbots are becoming a nuisance on fori such as Stack Exchange. To illustrate the nuisance capacity, here is a question / answer I produced there:

It sounds completely correct except for the core issue of not explaining why the Uniform density is not expressible as an exponential… And the answer is exactly the same when substituting Gamma for Uniform!

## stats postdoc in Barcelona

Posted in Statistics, Travel, University life with tags , , , , , , , , , , , , on April 5, 2022 by xi'an

Here is a call for exciting postdoc positions in high-dimensional statistics for network & graphical models analysis, Barcelona:

We have two post-doctoral positions to work on a range of topics related to high-dimensional statistics for networks, ultra high-dimensional graphical models, frameworks linking networks and graphical models, multivariate structural learning and time series analysis. The positions are for 1 year, with a potential for extension to 18 months, with a gross yearly salary of 40,000€. The scope is ample and allows for sub-projects related to mathematical statistics and statistical learning theory, data analysis methodology in penalized likelihood and Bayesian statistics, and computational methods. The positions are related to a Huawei grant, which also offers opportunities to explore applications of the developed theory & methods.

The project is primarily hosted by the Statistics group at UPF and the BSE Data Science Center in Barcelona (Spain), and is in collaboration with Luc Devroye at McGill University in Montreal (Canada) and Piotr Zwiernik at the University of Toronto (Canada). The primary supervisors are Christian Brownlees, Luc Devroye, Gábor Lugosi, David Rossell and Piotr Zwiernik, although collaborations with other professors of these research groups are also possible.

Interested candidates should send an updated CV and a short research statement to David Rossell (david.rossell AT upf.edu). They should ask 3 referees to send a letter of reference on their behalf.

The deadline for applying for the first position is April 30 2022, the deadline for the second position is June 15 2022.

## Bill’s 80th birthday

Posted in Statistics, Travel, University life with tags , , , , , , , , , , on March 30, 2022 by xi'an

## max vs. min

Posted in Books, Kids, Statistics with tags , , , , , , , , on March 26, 2022 by xi'an

Another intriguing question on X validated (about an exercise in Jun Shao’s book) that made me realise a basic fact about exponential distributions. When considering two Exponential random variables X and Y with possibly different parameters λ and μ,  Z⁺=max{X,Y} is dependent on the event X>Y while Z⁻=min{X,Y} is not (and distributed as an Exponential variate with parameter λ+μ.) Furthermore, Z⁺ is distributed from a signed mixture

$\frac{\lambda+\mu}{\mu}\mathcal Exp(\lambda)-\frac{\lambda}{\mu}\mathcal Exp(\lambda+\mu)$

conditionally on the event X>Y, meaning that there is no sufficient statistic of fixed dimension when given a sample of n realisations of Z⁺’s along with the indicators of the events X>Y…. This may explain why there exists an unbiased estimator of λ⁻¹-μ⁻¹ in this case and (apparently) not when replacing Z⁺ by Z⁻. (Even though the exercise asks for the UMVUE.)