Archive for exercises

I thought I did make a mistake but I was wrong…

Posted in Books, Kids, Statistics with tags , , , , , , , , , , , , on November 14, 2018 by xi'an

One of my students in my MCMC course at ENSAE seems to specialise into spotting typos in the Monte Carlo Statistical Methods book as he found an issue in every problem he solved! He even went back to a 1991 paper of mine on Inverse Normal distributions, inspired from a discussion with an astronomer, Caroline Soubiran, and my two colleagues, Gilles Celeux and Jean Diebolt. The above derivation from the massive Gradsteyn and Ryzhik (which I discovered thanks to Mary Ellen Bock when arriving in Purdue) is indeed incorrect as the final term should be the square root of 2β rather than 8β. However, this typo does not impact the normalising constant of the density, K(α,μ,τ), unless I am further confused.

back to the Bayesian Choice

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , on October 17, 2018 by xi'an

Surprisingly (or not?!), I received two requests about some exercises from The Bayesian Choice, one from a group of students from McGill having difficulties solving the above, wondering about the properness of the posterior (but missing the integration of x), to whom I sent back this correction. And another one from the Czech Republic about a difficulty with the term “evaluation” by which I meant (pardon my French!) estimation.

done! [#2]

Posted in Kids, Statistics, University life with tags , , , , , , , , , on January 21, 2016 by xi'an

exosPhew! I just finished my enormous pile of homeworks for the computational statistics course… This massive pile is due to an unexpected number of students registering for the Data Science Master at ENSAE and Paris-Dauphine. As I was not aware of this surge, I kept to my practice of asking students to hand back solved exercises from Monte Carlo Statistical Methods at the beginning of each class. And could not change the rules of the game once the course had started! Next year, I’ll make sure to get some backup for grading those exercises. Or go for group projects instead…

triste célébration for World Statistics Day

Posted in Books, Kids, Statistics, University life with tags , , , , on October 21, 2015 by xi'an

As I was discussing yesterday night with my daughter about a practice stats exam she had just taken in medical school, I came upon the following question:

What is the probability that women have the same risk of cancer as men in the entire population given that the selected sample concluded against equality?

Which just means nothing, since conditioning on the observed event, say |X|>1.96, cancels any probabilistic structure in the problem. Worse, I have no idea what is the expected answer to this question!

the travelling salesman

Posted in Statistics with tags , , , , , , , , on January 3, 2015 by xi'an

IMG_1099A few days ago, I was grading my last set of homeworks for the MCMC graduate course I teach to both Dauphine and ENSAE graduate students. A few students had chosen to write a travelling salesman simulated annealing code (Exercice 7.22 in Monte Carlo Statistical Methods) and one of them included this quote

“And when I saw that, I realized that selling was the greatest career a man could want. ‘Cause what could be more satisfying than to be able to go, at the age of eighty-four, into twenty or thirty different cities, and pick up a phone, and be remembered and loved and helped by so many different people ?”
Arthur Miller, Death of a Salesman

which was a first!

prayers and chi-square

Posted in Books, Kids, Statistics, University life with tags , , , , , , on November 25, 2014 by xi'an

One study I spotted in Richard Dawkins’ The God delusion this summer by the lake is a study of the (im)possible impact of prayer over patient’s recovery. As a coincidence, my daughter got this problem in her statistics class of last week (my translation):

1802 patients in 6 US hospitals have been divided into three groups. Members in group A was told that unspecified religious communities would pray for them nominally, while patients in groups B and C did not know if anyone prayed for them. Those in group B had communities praying for them while those in group C did not. After 14 days of prayer, the conditions of the patients were as follows:

  • out of 604 patients in group A, the condition of 249 had significantly worsened;
  • out of 601 patients in group B, the condition of 289 had significantly worsened;
  • out of 597 patients in group C, the condition of 293 had significantly worsened.

 Use a chi-square procedure to test the homogeneity between the three groups, a significant impact of prayers, and a placebo effect of prayer.

This may sound a wee bit weird for a school test, but she is in medical school after all so it is a good way to enforce rational thinking while learning about the chi-square test! (Answers: [even though the data is too sparse to clearly support a decision, esp. when using the chi-square test!] homogeneity and placebo effect are acceptable assumptions at level 5%, while the prayer effect is not [if barely].)

Emails I cannot reply to

Posted in Books, Statistics with tags , , , on May 26, 2010 by xi'an

I received this email yesterday from a reader of The Bayesian Choice (still selling on Amazon at a bargain price of  $32.97!)

can you guid me about  following  question kindly please? in  your  book “the bayesian choice ” chap.2 problem 2.45 asked :
if x has gamma distribution with shap parameter alpha and scale parameter tetha , and tetha has gamma distribution  with “v ” and “x0” parameters as shape and scale parameters show that bayes estimatore of tetha under Hellinger loss function is of the form of “k/(x+x0)”
if  we calculate Hellinger loss function for this distribution we see a loss function with nearly beta distribution.
i tried to earn this answer for bayes estimator ,but i could not  see this answer, can u give me a hint for this question?

Alas (?) I obviously cannot reply without providing the answer…. Of course, if there is a problem with this exercise, just let me know! But once you write down the Hellinger loss as

\text{L}(\theta,\delta) = 1 - \int \sqrt{ f_\theta(x) \,f_\delta(x) } \,\text{d}x

the remainder of the exercise is sheer calculus…