Archive for Monte Carlo integration

a neat (theoretical) Monte Carlo result

Posted in Books, Statistics, University life with tags , , , , on December 19, 2014 by xi'an

Mark Huber just arXived a short paper where he develops a Monte Carlo approach that bounds the probability of large errors

\mathbb{P}(|\hat\mu_t-\mu|>\epsilon\mu) < 1/\delta

by computing a lower bound on the sample size r and I wondered at the presence of μ in the bound as it indicates the approach is not translation invariant. One reason is that the standard deviation of the simulated random variables is bounded by cμ. Another reason is that Mark uses as its estimator the median

\text{med}(S_1R_1,\ldots,S_tR_t)

where the S’s are partial averages of sufficient length and the R’s are independent uniforms over (1-ε,1+ε): using those uniforms may improve the coverage of given intervals but it also means that the absolute scale of the error is multiplied by the scale of S, namely μ. I first thought that some a posteriori recentering could improve the bound but since this does not impact the variance of the simulated random variables, I doubt it is possible.

R midterms

Posted in Kids, Linux, R, Statistics, University life with tags , , , , , , , , , , , on November 9, 2012 by xi'an

Here are my R midterm exams, version A and version B in English (as students are sitting next to one another in the computer rooms), on simulation methods for my undergrad exploratory statistics course. Nothing particularly exciting or innovative! Dedicated ‘Og‘s readers may spot a few Le Monde puzzles in the lot…

Two rather entertaining if mundane occurences related to this R exam: one hour prior to the exam, a student came to my office to beg for being allowed to take the solution manual with her (as those midterm exercises are actually picked from an exercise booklet, some students cooperated towards producing a complete solution manual and this within a week!), kind of missing the main point of having an exam. (I have not seen yet this manual but I’d be quite interested in checking the code they produced on that occasion…) During the exam, another student asked me what was the R command to turn any density into a random generator: he had written a density function called mydens and could not fathom why rmydens(n) was not working. The same student later called me as his computer was “stuck”: he was not aware that a “+” prompt on the command line meant R was waiting for him to complete the command… A less comical event that ended well is that a student failed to save her R code (periodically and) at the end of the exam and we had to dig very deep into the machine to salvage her R commands from \tmp as rkward safeguards, as only the .RData file was available at first. I am glad we found this before turning the machine off, otherwise it would have been lost.

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