Archive for the R Category

MCMskv, Lenzerheide, Jan. 5-7, 2016

Posted in Kids, Mountains, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , on March 31, 2015 by xi'an

moonriseFollowing the highly successful [authorised opinion!, from objective sources] MCMski IV, in Chamonix last year, the BayesComp section of ISBA has decided in favour of a two-year period, which means the great item of news that next year we will meet again for MCMski V [or MCMskv for short], this time on the snowy slopes of the Swiss town of Lenzerheide, south of Zürich. The committees are headed by the indefatigable Antonietta Mira and Mark Girolami. The plenary speakers have already been contacted and Steve Scott (Google), Steve Fienberg (CMU), David Dunson (Duke), Krys Latuszynski (Warwick), and Tony Lelièvre (Mines, Paris), have agreed to talk. Similarly, the nine invited sessions have been selected and will include Hamiltonian Monte Carlo,  Algorithms for Intractable Problems (ABC included!), Theory of (Ultra)High-Dimensional Bayesian Computation, Bayesian NonParametrics, Bayesian Econometrics,  Quasi Monte Carlo, Statistics of Deep Learning, Uncertainty Quantification in Mathematical Models, and Biostatistics. There will be afternoon tutorials, including a practical session from the Stan team, tutorials for which call is open, poster sessions, a conference dinner at which we will be entertained by the unstoppable Imposteriors. The Richard Tweedie ski race is back as well, with a pair of Blossom skis for the winner!

As in Chamonix, there will be parallel sessions and hence the scientific committee has issued a call for proposals to organise contributed sessions, tutorials and the presentation of posters on particularly timely and exciting areas of research relevant and of current interest to Bayesian Computation. All proposals should be sent to Mark Girolami directly by May the 4th (be with him!).

intuition beyond a Beta property

Posted in Books, Kids, R, Statistics, University life with tags , , , on March 30, 2015 by xi'an

betas

A self-study question on X validated exposed an interesting property of the Beta distribution:

If x is B(n,m) and y is B(n+½,m) then √xy is B(2n,2m)

While this can presumably be established by a mere change of variables, I could not carry the derivation till the end and used instead the moment generating function E[(XY)s/2] since it naturally leads to ratios of B(a,b) functions and to nice cancellations thanks to the ½ in some Gamma functions [and this was the solution proposed on X validated]. However, I wonder at a more fundamental derivation of the property that would stem from a statistical reasoning… Trying with the ratio of Gamma random variables did not work. And the connection with order statistics does not apply because of the ½. Any idea?

Le Monde puzzle [#904.5]

Posted in Books, Kids, R, Statistics, University life with tags , , , on March 25, 2015 by xi'an

About this #904 arithmetics Le Monde mathematical puzzle:

Find all plural integers, namely positive integers such that (a) none of their digits is zero and (b) removing their leftmost digit produces a dividing plural integer (with the convention that one digit integers are all plural).

a slight modification in the R code allows for a faster exploration, based on the fact that solutions add one extra digit to solutions with one less digit:

First, I found this function on Stack Overflow to turn an integer into its digits:

pluri=plura=NULL
#solutions with two digits
for (i in 11:99){

 dive=rev(digin(i)[-1])
 if (min(dive)>0){
 dive=sum(dive*10^(0:(length(dive)-1)))
 if (i==((i%/%dive)*dive))
 pluri=c(pluri,i)}}

for (n in 2:6){ #number of digits
  plura=c(plura,pluri)
  pluro=NULL
  for (j in pluri){

   for (k in (1:9)*10^n){
     x=k+j
     if (x==(x%/%j)*j)
       pluro=c(pluro,x)}
   }
   pluri=pluro}

which leads to the same output

> sort(plura)
 [1] 11 12 15 21 22 24 25 31 32 33 35 36
[13] 41 42 44 45 48 51 52 55 61 62 63 64
[25] 65 66 71 72 75 77 81 82 84 85 88 91
[37] 92 93 95 96 99 125 225 312 315 325 375 425
[49] 525 612 615 624 625 675 725 735 825 832 912 
[61] 915 925 936 945 975 1125 2125 3125 3375 4125 
[70] 5125 5625 
[72] 6125 6375 7125 8125 9125 9225 9375 53125 
[80] 91125 95625

The synoptic problem and statistics [book review]

Posted in Books, R, Statistics, University life, Wines with tags , , , , , , , , , , , , on March 20, 2015 by xi'an

A book that came to me for review in CHANCE and that came completely unannounced is Andris Abakuks’ The Synoptic Problem and Statistics.  “Unannounced” in that I had not heard so far of the synoptic problem. This problem is one of ordering and connecting the gospels in the New Testament, more precisely the “synoptic” gospels attributed to Mark, Matthew and Luke, since the fourth canonical gospel of John is considered by experts to be posterior to those three. By considering overlaps between those texts, some statistical inference can be conducted and the book covers (some of?) those statistical analyses for different orderings of ancestry in authorship. My overall reaction after a quick perusal of the book over breakfast (sharing bread and fish, of course!) was to wonder why there was no mention made of a more global if potentially impossible approach via a phylogeny tree considering the three (or more) gospels as current observations and tracing their unknown ancestry back just as in population genetics. Not because ABC could then be brought into the picture. Rather because it sounds to me (and to my complete lack of expertise in this field!) more realistic to postulate that those gospels were not written by a single person. Or at a single period in time. But rather that they evolve like genetic mutations across copies and transmission until they got a sort of official status.

“Given the notorious intractability of the synoptic problem and the number of different models that are still being advocated, none of them without its deficiencies in explaining the relationships between the synoptic gospels, it should not be surprising that we are unable to come up with more definitive conclusions.” (p.181)

The book by Abakuks goes instead through several modelling directions, from logistic regression using variable length Markov chains [to predict agreement between two of the three texts by regressing on earlier agreement] to hidden Markov models [representing, e.g., Matthew’s use of Mark], to various independence tests on contingency tables, sometimes bringing into the model an extra source denoted by Q. Including some R code for hidden Markov models. Once again, from my outsider viewpoint, this fragmented approach to the problem sounds problematic and inconclusive. And rather verbose in extensive discussions of descriptive statistics. Not that I was expecting a sudden Monty Python-like ray of light and booming voice to disclose the truth! Or that I crave for more p-values (some may be found hiding within the book). But I still wonder about the phylogeny… Especially since phylogenies are used in text authentication as pointed out to me by Robin Ryder for Chauncer’s Canterbury Tales.

the vim cheat sheet

Posted in Kids, Linux, R, University life, Wines with tags , , , on March 18, 2015 by xi'an

amazing Gibbs sampler

Posted in Books, pictures, R, Statistics, University life with tags , , , , , , on February 19, 2015 by xi'an

BayesmWhen playing with Peter Rossi’s bayesm R package during a visit of Jean-Michel Marin to Paris, last week, we came up with the above Gibbs outcome. The setting is a Gaussian mixture model with three components in dimension 5 and the prior distributions are standard conjugate. In this case, with 500 observations and 5000 Gibbs iterations, the Markov chain (for one component of one mean of the mixture) has two highly distinct regimes: one that revolves around the true value of the parameter, 2.5, and one that explores a much broader area (which is associated with a much smaller value of the component weight). What we found amazing is the Gibbs ability to entertain both regimes, simultaneously.

MissData 2015 in Rennes [June 18-19]

Posted in R, Statistics, Travel, University life with tags , , , , , , on February 9, 2015 by xi'an

This (early) summer, a conference on missing data will be organised in Rennes, Brittany, with the support of the French Statistical Society [SFDS]. (Check the website if interested, Rennes is a mere two hours from Paris by fast train.)

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