Introduction to Monte Carlo methods with R and Bayesian Essentials with R

Here are the  download figures for my e-book with George as sent to me last week by my publisher Springer-Verlag.  With an interesting surge in the past year. Maybe simply due to new selling strategies of the published rather to a wider interest in the book. (My royalties have certainly not increased!) Anyway thanks to all readers. As an aside for wordpress wannabe bloggers, I realised it is now almost impossible to write tables with WordPress, another illustration of the move towards small-device-supported blogs. Along with a new annoying “simpler” (or more accurately dumber) interface and a default font far too small for my eyesight. So I advise alternatives to wordpress that are more sympathetic to maths contents (e.g., using MathJax) and comfortable editing.

And the same for the e-book with Jean-Michel, which only appeared in late 2013. And contains more chapters than Introduction to Monte Carlo methods with R. Incidentally, a reader recently pointed out to me the availability of a pirated version of The Bayesian Choice on a Saudi (religious) university website. And of a pirated version of Introducing Monte Carlo with R on a Saõ Paulo (Brazil) university website. This may be alas inevitable, given the diffusion by publishers of e-chapters that can be copied with no limitations…

Buffon needled R exams

Here are two exercises I wrote for my R mid-term exam in Paris-Dauphine around Buffon’s needle problem. In the end, the problems sounded too long and too hard for my 3rd year students so I opted for softer questions. So recycle those if you wish (but do not ask for solutions!)

slides for my simulation course

Similar to last year, I am giving a series of lectures on simulation jointly as a Master course in Paris-Dauphine and as a 3rd year course in ENSAE. The course borrows from both the books Monte Carlo Statistical Methods and from Introduction to Monte Carlo Methods with R, with George Casella. Here are the three series of slides I will use throughout the course this year, mostly for the benefit of the students:

(the last series is much improved when compared with an earlier version, thanks to Olivier Cappé!)

R exam

Following a long tradition (!) of changing the modus vivendi of each exam in our exploratory statistics with R class, we decided this year to give the students a large collection of exercises prior to the exam and to pick five among them to the exam, the students having to solve two and only two of them. (The exercises are available in French on my webpage.) This worked beyond our expectations in that the overwhelming majority of students went over all the exercises and did really (too) well at the exam! Next year, we will hopefully increase the collection of exercises and also prohibit written notes during the exam (to avoid a possible division of labour among the students).

Incidentally, we found a few (true) gems in the solutions, incl. an harmonic mean resolution of the approximation of the integral

since some students generated from the distribution with density f proportional to the integrand over [2,∞) [a truncated gamma] and then took the estimator

although we expected them to simulate directly from the exponential and average the sample to the fourth power… In this specific situation, the (dreaded) harmonic mean estimator has a finite variance! To wit;

> y=rgamma(shape=5,n=10^5)
> pgamma(2,5,low=FALSE)*gamma(5)
[1] 22.73633
> integrate(f=function(x){x^4*exp(-x)},2,Inf)
22.73633 with absolute error < 0.0017
> pgamma(2,1,low=FALSE)/mean(y[y>2]^{-4})
[1] 22.92461
> z=rgamma(shape=1,n=10^5)
> mean((z>2)*z^4)
[1] 23.92876

So the harmonic means does better than the regular Monte Carlo estimate in this case!

Méthodes de Monte-Carlo avec R [out]

The translation of the book Introducing Monte Carlo Methods with R is now published and out! I have received five copies in the mail yesterday, although it was not produced in time for my R class students to get it before the exam today. The book is still indicated on amazon.com as appearing in February, while amazon.fr announces the publication for January 20. I am very pleased with the quality of the output, in contrast with the first printing of the English version.