Publications by xi'an
BayesComp 20 [schedule]
The schedule for the program is now available on the conference webpage of BayesComp 20, for the days of 7-10 Jan 2020. There are twelve invited sessions, including one j-ISBA session, and a further thirteen contributed sessions were selected by the scientific committee. And three tutorials on the first day. Looking forward seeing you in Florida!...
782 sym 2 img
Froebenius coin problem
A challenge from The Riddler last weekend came out as the classical Frobenius coin problem, namely to find the largest amount that cannot be obtained using only n coins of specified coprime denominations (i.e., with gcd equal to one). There is always such a largest value. For the units a=19 and b=538, I ran a basic R code that returned 9665 as th...
1929 sym R (81 sym/1 pcs) 6 img
riddle by attrition
The weekend riddle from The Riddler is rather straightforward [my wording and simplification]: Construct a decimal number X between 0 and 1 by drawing the first digit a¹ uniformly over {0,1,…,9}, the second digit a² uniformly over {0,1,…,9}, &tc., until 0 is attained. What is the expectation of this random variable X? Since each new digit h...
941 sym R (110 sym/1 pcs) 2 img
Le Monde puzzle [#1119]
A digit puzzle as Le weekly Monde current mathematical puzzle that sounds close to some earlier versions: Perfect squares are pairs (a²,b²) with the same number of digits such that a²b² is itself a square. What is the pair providing a²b² less than 10⁶? Is there a solution with both integers enjoying ten digits? The run of a brute force ...
963 sym R (307 sym/2 pcs) 2 img
sampling the mean
A challenge found on the board of the coffee room at CEREMADE, Université Paris Dauphine: When sampling with replacement three numbers in {0,1,…,N}, what is the probability that their average is (at least) one of the three? With a (code-golfed!) brute force solution of mean(!apply((a<-sample(0:n,3e6,rep=T),3)),2,mean)-apply(a,2,median)) pro...
773 sym R (69 sym/1 pcs) 2 img
an arithmetic mean identity
A 2017 paper by Ana Pajor published in Bayesian Analysis addresses my favourite problem [of computing the marginal likelihood] and which I discussed on the ‘Og, linking with another paper by Lenk published in 2012 in JCGS. That I already discussed here last year. Lenk’s (2009) paper is actually using a technique related to the harmonic mean c...
2637 sym R (78 sym/1 pcs) 2 img
riddle on a circle
The Riddler’s riddle this week provides another opportunity to resort to brute-force simulated annealing! Given a Markov chain defined on the torus {1,2,…,100} with only moves a drift to the right (modulo 100) and a uniformely random jump, find the optimal transition matrix to reach 42 in a minimum (average) number of moves. Which I coded i...
1155 sym R (280 sym/1 pcs)
postdoc in Bayesian machine learning in Berlin [reposted]
The working group of Statistics at Humboldt University of Berlin invites applications for one Postdoctoral research fellow (full-time employment, 3 years with extension possible) to contribute to the research on mathematical and statistical aspects of (Bayesian) learning approaches. The research positions are associated with the Emmy Noether grou...
3533 sym 2 img
Le Monde puzzle [#1124]
A prime number challenge [or rather two!] as Le weekly Monde current mathematical puzzle: When considering the first two integers, 1 and 2, their sum is 3, a prime number. For the first four integers, 1,2,3,4, it is again possible to sum them pairwise to obtain two prime numbers, eg 3 and 7. Up to which limit is this operation feasible? And how ...
1129 sym R (127 sym/2 pcs) 2 img
Metropolis in 95 characters
Here is an R function that produces a Metropolis-Hastings sample for the univariate log-target f when the later is defined outside as another function. And when using a Gaussian random walk with scale one as proposal. (Inspired from a X validated question.) m<-function(T,y=rnorm(1))ifelse(rep(T>1,T), c(y*{f({z<-m(T-1)}[1])-f(y+z[1])<rexp(1)}+z...
922 sym R (101 sym/1 pcs) 2 img