Archive for Vercors

splitting a field by annealing

Posted in Kids, pictures, R, Statistics with tags , , , , , , , , on October 18, 2017 by xi'an

A recent riddle [from The Riddle] that I pondered about during a [long!] drive to Luxembourg last weekend was about splitting a square field into three lots of identical surface for a minimal length of separating wire… While this led me to conclude that the best solution was a T like separation, I ran a simulated annealing R code on my train trip to AutransValence, seemingly in agreement with this conclusion.I discretised the square into n² units and explored configurations by switching two units with different colours, according to a simulated annealing pattern (although unable to impose connectivity on the three regions!):

partz=matrix(1,n,n)
partz[,1:(n/3)]=2;partz[((n/2)+1):n,((n/3)+1):n]=3
#counting adjacent units of same colour 
nood=hood=matrix(4,n,n)
for (v in 1:n2) hood[v]=bourz(v,partz)
minz=el=sum(4-hood)
for (t in 1:T){
  colz=sample(1:3,2) #picks colours
  a=sample((1:n2)[(partz==colz[1])&(hood<4)],1)
  b=sample((1:n2)[(partz==colz[2])&(hood<4)],1) 
  partt=partz;partt[b]=colz[1];partt[a]=colz[2] 
#collection of squares impacted by switch 
  nood=hood 
  voiz=unique(c(a,a-1,a+1,a+n,a-n,b-1,b,b+1,b+n,b-n)) 
  voiz=voiz[(voiz>0)&(voiz<n2)] 
  for (v in voiz) nood[v]=bourz(v,partt) 
  if (nood[a]*nood[b]>0){
    difz=sum(nood)-sum(hood)
    if (log(runif(1))<difz^3/(n^3)*(1+log(10*rep*t)^3)){
      el=el-difz;partz=partt;hood=nood     
      if (el<minz){ minz=el;cool=partz}
  }}}

(where bourz computes the number of neighbours), which produces completely random patterns at high temperatures (low t) and which returns to the T configuration (more or less):if not always, as shown below:Once the (a?) solution was posted on The Riddler, it appeared that one triangular (Y) version proved better than the T one [if not started from corners], with a gain of 3% and that a curved separation was even better with an extra gain less than 1% [solution that I find quite surprising as straight lines should improve upon curved ones…]

Astrostatistics school

Posted in Mountains, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , on October 17, 2017 by xi'an

What a wonderful week at the Astrostat [Indian] summer school in Autrans! The setting was superb, on the high Vercors plateau overlooking both Grenoble [north] and Valence [west], with the colours of the Fall at their brightest on the foliage of the forests rising on both sides of the valley and a perfect green on the fields at the centre, with sun all along, sharp mornings and warm afternoons worthy of a late Indian summer, too many running trails [turning into X country ski trails in the Winter] to contemplate for a single week [even with three hours of running over two days], many climbing sites on the numerous chalk cliffs all around [but a single afternoon for that, more later in another post!]. And of course a group of participants eager to learn about Bayesian methodology and computational algorithms, from diverse [astronomy, cosmology and more] backgrounds, trainings and countries. I was surprised at the dedication of the participants travelling all the way from Chile, Péru, and Hong Kong for the sole purpose of attending the school. David van Dyk gave the first part of the school on Bayesian concepts and MCMC methods, Roberto Trotta the second part on Bayesian model choice and hierarchical models, and myself a third part on, surprise, surprise!, approximate Bayesian computation. Plus practicals on R.

As it happens Roberto had to cancel his participation and I turned for a session into Christian Roberto, presenting his slides in the most objective possible fashion!, as a significant part covered nested sampling and Savage-Dickey ratios, not exactly my favourites for estimating constants. David joked that he was considering postponing his flight to see me talk about these, but I hope I refrained from engaging into controversy and criticisms… If anything because this was not of interest for the participants. Indeed when I started presenting ABC through what I thought was a pedestrian example, namely Rasmus Baath’s socks, I found that the main concern was not running an MCMC sampler or a substitute ABC algorithm but rather an healthy questioning of the construction of the informative prior in that artificial setting, which made me quite glad I had planned to cover this example rather than an advanced model [as, e.g., one of those covered in the packages abc, abctools, or abcrf]. Because it generated those questions about the prior [why a Negative Binomial? why these hyperparameters? &tc.] and showed how programming ABC turned into a difficult exercise even in this toy setting. And while I wanted to give my usual warning about ABC model choice and argue for random forests as a summary selection tool, I feel I should have focussed instead on another example, as this exercise brings out so clearly the conceptual difficulties with what is taught. Making me quite sorry I had to leave one day earlier. [As did missing an extra run!] Coming back by train through the sunny and grape-covered slopes of Burgundy hills was an extra reward [and no one in the train commented about the local cheese travelling in my bag!]

 

Autrans, Vercors [jatp]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , on October 16, 2017 by xi'an

Gorges de la Bourne [jatp]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , , on October 12, 2017 by xi'an

[Astrostat summer school] fogrise [jatp]

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2017 by xi'an

[Astrostat summer school] sunrise [jatp]

Posted in Statistics with tags , , , , , , , , , , , on October 10, 2017 by xi'an

[summer Astrostat school] room with a view [jatp]

Posted in Mountains, pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , on October 9, 2017 by xi'an

I just arrived in Autrans, on the Plateau du Vercors overlooking Grenoble and the view is fabulistic! Trees have started to turn red and yellow, the weather is very mild, and my duties are restricted to teaching ABC to a group of enthusiastic astronomers and cosmologists..! Second advanced course on ABC in the mountains this year, hard to beat (except by a third course). The surroundings are so serene and peaceful that I even conceded to install RStudio for my course! Instead of sticking to my favourite vim editor and line commands.