the never-ending summer of Bayesian conferences!

Posted in Books, Kids, Mountains, pictures, Statistics, Travel, University life, Wines on March 9, 2018 by xi'an

In addition to the various Bayesian and MC(q)MC conferences, workshops, and summer schools already signaled here, here is another announcement about a summer school on Bayesian Statistics in Sports, on 4-8 June 2018, which is delivered by Kerrie Mengersen (QUT, Brisbane). As detailed on the webpage for the school, the training takes place on Lago di Como, and is the current edition of the Applied Bayesian Statistics summer school. Registration is open.

StanCon in Helsinki [29-31 Aug 2018]

Posted in Books, pictures, R, Statistics, Travel, University life with tags , , , , , , , , on March 7, 2018 by xi'an

As emailed to me by Aki Vehtari, the next StanCon will take place this summer in the wonderful city of Helsinki, at the end of August. On Aalto University Töölö Campus precisely. The list of speakers and tutorial teachers is available on the webpage. (The only “negative point” is that the conference does not include a Tuesday, the night of the transcendence 2 miles race!) Somewhat concluding this never-ending summer of Bayesian conferences!

a one-chance meeting [puzzle]

Posted in Books, Kids, pictures, R with tags , , , , , , on March 6, 2018 by xi'an

This afternoon, I took a quick look at the current Riddler puzzle, which sums up as, given three points A, B, C, arbitrarily moving on a plane with a one-shot view of their respective locations, find a moving rule to bring the three together at the same point at the same time. And could not spot the difficulty.

The solution seems indeed obvious when expressed as above rather than in the tell-tale format of the puzzle. Since every triangle has a circumscribed circle, and all points on that circle are obviously at the same distance of the centre O, the three points have to aim at the centre O. Assuming they all move at the same velocity, they will reach O together…

The question gets a wee bit more interesting when the number of points with the same one-time one-shot view option grows beyond 3, as these points will almost surely not all lie on a single circumscribed circle. While getting them together can be done by (a) finding the largest circle going through 3  points and containing all others [in case there is no such circle, adding an artificial point solves the issue!], triplet on which one can repeat the above instructions to reach O, and (b) bringing all points inside the circle to meet with one of the three points [the closest] on its straight-line way to O, by finding a point on that line at equal distance from both, a subsidiary question is whether or not this is the fastest way. Presumably not.  (Again I may be missing one item of the puzzle.)

When experimenting with a short R code, I quickly figured out that the circumscribed circles associated with all triplets do not necessarily contain all points. The resolution of this difficulty is however straightforward as it suffices to add an artificial point by considering all circumcentres and their distances to the farthest point, minimising over these distances and adding the extra point at random over the circumference. As in the example below.Incidentally, it took me much longer to write this post than to solve the puzzle, as I was trying to use the R function draw.circle, which supposedly turns a centre and a radius into the corresponding circle, but somehow misses its target by adapting the curve to the area being displayed. I am still uncertain of what the function means. I hence ended up writing a plain R function for this purpose:

dracirc=function(A,B,C){
O=findcentr(A,B,C)
ro=dist(rbind(A,O))
lines(x=O[1]+ro*sin(2*pi*seq(0,1,le=180)),
y=O[2]+ro*cos(2*pi*seq(0,1,le=180)))}


Le Monde puzzle [#1043]

Posted in Books, Kids with tags , , , , , , on March 5, 2018 by xi'an

An arithmetic Le Monde mathematical puzzle :

A number is “noble” if all its digits are different and if it is equal to the average of all numbers created by permuting its digits. What are the noble numbers?

There is no need for simulation when plain enumeration works. After failing to install the R packge permutations, I installed the R package permute, which works, although (a) the function allPerm does not apply directly to a vector of characters or numbers but only to its size:

> allPerms(c("a","r","h"))
[,1] [,2] [,3]
[1,]    1    3    2
[2,]    2    1    3
[3,]    2    3    1
[4,]    3    1    2
[5,]    3    2    1


and (b) as seen above the function does not contain “all” permutations since it misses the identity permutation.  Which ends up being fine for solving this puzzle. Using a bit of digit-character manipulation

findzol=function(N=2){
for (u in 1:(10^N-1)){
digz=strsplit(as.character(u),"")[[1]]
if (length(digz)<N)
digz=c(rep("0",N-length(digz)),digz)
if (length(unique(digz))==N){
permz=apply(matrix(digz[allPerms(1:N)],
ncol=N),2,as.numeric)
if (mean(permz%*%10^{(N-1):0})==u) print(u)}}}


I found solutions for N=3

> findzol(3)
[1] 370
[1] 407
[1] 481
[1] 518
[1] 592
[1] 629


and none for N=4,5,6. Le Monde gives solutions for N=9, which is not achievable by my code!

A discovery of wromynce

Posted in Books, Travel, University life with tags , , , on March 4, 2018 by xi'an

While recovering from this minor food poisoning bout in Oxford the other week, I took a break by having an early night after my class and reading a book hurriedly purchase from a local bookstore, A Discovery of Witches, by Deborah Harkness, which title sounded (wrongly) familiar, and which turned out to be a soapy wromynce (my own mix of witch, vampyre, and romance…) involving a reluctant witch and a very ancient vampyre falling in love against the eternal rules of their respective communities. Including all imaginable clichés on these creatures, like enormous wealth, superior intelligence, involvement into human history, science, arts, politics, &tc., since the dawn of time (at the very least). The style is appalling, with one dimensional characters and less-than-one-dimension plots, a hotchpotch of alchemy and the most advanced science, of historical facts and of the most threadbare conspiracy theories, the main character oscillating between the rational, precocious, sport-obsessed, Oxford academic and a Harlequin-like damsel-in-distress having lost her intellectual pursuits… As in La Belle Sauvage, the book has a strong connection with Oxford and its colleges at the beginning of the book that may make for an extra incentive, but it was a relief to abandon the unfinished book there before returning to Paris|

ABCDay [arXivals]

Posted in Books, Statistics, University life with tags , , , , , , on March 2, 2018 by xi'an

A bunch of ABC papers on arXiv yesterday, most of them linked to the incoming Handbook of ABC:

1. Overview of Approximate Bayesian Computation S. A. Sisson, Y. Fan, M. A. Beaumont
2. Kernel Recursive ABC: Point Estimation with Intractable Likelihood Takafumi Kajihara, Keisuke Yamazaki, Motonobu Kanagawa, Kenji Fukumizu
3. High-dimensional ABC D. J. Nott, V. M.-H. Ong, Y. Fan, S. A. Sisson
4. ABC Samplers Y. Fan, S. A. Sisson

an interesting identity

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , on March 1, 2018 by xi'an

Another interesting X validated question, another remembrance of past discussions on that issue. Discussions that took place in the Institut d’Astrophysique de Paris, nearby this painting of Laplace, when working on our cosmostats project. Namely the potential appeal of recycling multidimensional simulations by permuting the individual components in nearly independent settings. As shown by the variance decomposition in my answer, when opposing N iid pairs (X,Y) to the N combinations of √N simulations of X and √N simulations of Y, the comparison

$\text{var} \hat{\mathfrak{h}}^2_N=\text{var} (\hat{\mathfrak{h}}^1_N)+\frac{mn(n-1)}{N^2}\,\text{var}^Y\left\{ \mathbb{E}^{X}\left\{\mathfrak{h}(X,Y)\right\}\right\}$

$+\frac{m(m-1)n}{N^2}\,\text{var}^X\left[\mathbb{E}^Y\left\{\mathfrak{h}(X,Y)\right\}\right]$

unsurprisingly gives the upper hand to the iid sequence. A sort of converse to Rao-Blackwellisation…. Unless the production of N simulations gets much more costly when compared with the N function evaluations. No wonder we never see this proposal in Monte Carlo textbooks!