Archive for undergraduates

hands-on probability 101

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , on April 3, 2021 by xi'an


When solving a rather simple probability question on X validated, namely the joint uniformity of the pair

(X,Y)=(A-B+\mathbb I_{A<B},C-B+\mathbb I_{C<B})

when A,B,C are iid U(0,1), I chose a rather pedestrian way and derived the joint distribution of (A-B,C-B), which turns to be made of 8 components over the (-1,1)² domain. And to conclude at the uniformity of the above, I added a hand-made picture to explain why the coverage by (X,Y) of any (red) square within (0,1)² was uniform by virtue of the symmetry between the coverage by (A-B,C-B) of four copies of the (red) square, using color tabs that were sitting on my desk..! It did not seem to convince the originator of the question, who kept answering with more questions—or worse an ever-changing question, reproduced in real time on math.stackexchange!, revealing there that said originator was tutoring an undergrad student!—but this was a light moment in a dreary final day before a new lockdown.

a glaringly long explanation

Posted in Statistics with tags , , , , , , , , , , on December 19, 2018 by xi'an

It is funny that, when I am teaching the rudiments of Bayesian statistics to my undergraduate students in Paris-Dauphine, including ABC via Rasmus’ socks, specific questions about the book (The Bayesian Choice) start popping up on X validated! Last week was about the proof that ABC is exact when the tolerance is zero. And the summary statistic sufficient.

This week is about conjugate distributions for exponential families (not that there are many others!). Which led me to explain both the validation of the conjugacy and the derivation of the posterior expectation of the mean of the natural sufficient statistic in far more details than in the book itself. Hopefully in a profitable way.

done! [#1]

Posted in Kids, pictures, University life with tags , , , , , , on January 16, 2016 by xi'an

After spending a few hours grading my 127 exams for most nights of this week, I am finally done with it! One of the exam questions was the simulation of XY when (X,Y) is a bivariate normal vector with correlation ρ, following the trick described in a X validated question asked a few months ago, namely that

XY≡R{cos(πU)+ρ}

but no one managed to establish this representation. And, as usual, some students got confused between parameters θ and observations x when writing a posterior density, since the density of the prior was defined in the exam with the dummy x, thereby recovering the prior as the posterior. Nothing terrible and nothing exceptional with this cohort of undergraduates. And now I still have to go through my second pile of exams for the graduate course I taught on Bayesian computational tools…

Statistics second slides

Posted in Books, Kids, Statistics, University life with tags , , , , , on September 24, 2014 by xi'an

La Défense from Paris-Dauphine, Nov. 15, 2012This is the next chapter of my Statistics course, definitely more standard, with some notions on statistical models, limit theorems, and exponential families. In the first class, I recalled the convergence notions with no proof but counterexamples and spend some time on a slide not included here, borrowed from Chris Holmes’ talk last Friday on the linear relation between blood pressure and the log odds ratio of an heart condition. This was a great example, both to illustrate the power of increasing the number of observations and of using a logistic regression model. Students kept asking questions about it.

new kids on the block

Posted in Kids, R, Statistics, University life with tags , , , on September 22, 2014 by xi'an

La Defense, Dec. 10, 2010This summer, for the first time, I took three Dauphine undergraduate students into research projects thinking they had had enough R training (with me!) and several stats classes to undertake such projects. In all cases, the concept was pre-defined and “all they had to do” was running a massive flow of simulations in R (or whatever language suited them best!) to check whether or not the idea was sound. Unfortunately, for two projects, by the end of the summer, we had not made any progress in any of the directions I wanted to explore… Despite a fairly regular round of meetings and emails with those students. In one case the student had not even managed to reproduce the (fairly innocuous) method I wanted to improve upon. In the other case, despite programming inputs from me, the outcome was impossible to trust.  A mostly failed experiment which makes me wonder why it went that way. Granted that those students had no earlier training in research, either in exploiting the literature or in pushing experiments towards logical extensions. But I gave them entries, discussed with them those possible new pathways, and kept updating schedules and work-charts. And the students were volunteers with no other incentive than discovering research (I even had two more candidates in the queue).  So it may be (based on this sample of 3!) that our local training system is missing in this respect. Somewhat failing to promote critical thinking and innovation by imposing too long presence hours and by evaluating the students only through standard formalised tests. I do wonder, as I regularly see [abroad] undergraduate internships and seminars advertised in the stats journals. Or even conferences.

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