Filed under: pictures, Travel Tagged: black tea, China, fermented tea, Pu Erh tea, Yunnan ]]>

Filed under: pictures, Travel Tagged: 67P/Churyumov–Gerasimenko, astronomy, comets, European Space Agency, Philae lander, Rosetta, space probe ]]>

Does there exist a 3×3 grid with different and positive integer entries such that the sum of rows, columns, and both diagonals is a prime number? If there exist such grids, find the grid with the minimal sum?

**I **first downloaded the R package ** primes**. Then I checked if by any chance a small bound on the entries was sufficient:

cale<-function(seqe){ ros=apply(seqe,1,sum) cole=apply(seqe,2,sum) dyag=sum(diag(seqe)) dayg=sum(diag(seqe[3:1,1:3])) return(min(is_prime(c(ros,cole,dyag,dayg)))>0)}

Running the blind experiment

for (t in 1:1e6){ n=sample(9:1e2,1) if (cale(matrix(sample(n,9),3))) print(n)}

I got 10 as the minimal value of n. Trying with n=9 did not give any positive case. Running another blind experiment checking for the minimal sum led to the result

> A [,1] [,2] [,3] [1,] 8 3 6 [2,] 1 5 7 [3,] 2 11 4

with sum 47.

Filed under: Books, Kids, pictures, Statistics, Travel, University life Tagged: arithmetics, Le Monde, mathematical puzzle, prime number, primes, R, R package, sudoku ]]>

**H**ere are the slides of the presentation I gave at the EPSRC Advanced Computational methods for complex models in Biology at University College London, last week. Introducing random forests as proper summaries for both model choice and parameter estimation (with considerable overlap with earlier slides, obviously!). The other talks of that highly interesting day on computational Biology were mostly about ancestral graphs, using Wright-Fisher diffusions for coalescents, plus a comparison of expectation-propagation and ABC on a genealogy model by Mark Beaumont and the decision theoretic approach to HMM order estimation by Chris Holmes. In addition, it gave me the opportunity to come back to the Department of Statistics at UCL more than twenty years after my previous visit, at a time when my friend Costas Goutis was still there. And to realise it had moved from its historical premises years ago. (I wonder what happened to the two staircases built to reduce frictions between Fisher and Pearson if I remember correctly…)

Filed under: Books, pictures, Statistics, Travel, University life Tagged: ABC, Bayesian computing, Biology, coalescent, computational biology, England, EPSRC, expectation-propagation, London, random forests, UCL, University College London, Wright-Fisher model ]]>

Filed under: Statistics Tagged: Markov chain, Markov chain Monte Carlo algorithm, MCMC convergence, particle filter, pseudo-marginal MCMC, sequential Monte Carlo, University of Warwick ]]>

∫ φ(x) dx

when replacing the true importance distribution ƒ with a leave-one-out (!) kernel estimate in the importance sampling estimator… They also consider a debiased version that converges even faster at the rate

where n is the sample size, h the bandwidth and d the dimension. There is however a caveat, namely a collection of restrictive assumptions on the components of this new estimator:

- the integrand φ has a compact support, is bounded, and satisfies some Hölder-type regularity condition;
- the importance distribution ƒ is upper and lower bounded, its r-th order derivatives are upper bounded;
- the kernel K is order r, with exponential tails, and symmetric;
- the leave-one-out correction for bias has a cost O(n²) compared with O(n) cost of the regular Monte-Carlo estimator;
- the bandwidth h in the kernel estimator has a rate in n linked with the dimension d and the regularity indices of ƒ and φ

and this bandwidth needs to be evaluated as well. In the paper the authors rely on a control variate for which the integral is known, but which “looks like φ”, a strong requirement *in appearance only* since this new function is the convolution of φ with a kernel estimate of ƒ which expectation is the original importance estimate of the integral. This sounds convoluted but this is a generic control variate nonetheless! But this is also a costly step. Because of the kernel estimation aspect, the method deteriorates with the dimension of the variate x. However, since φ(x) is a real number, I wonder if running the non-parametric density estimate directly on the sample of φ(x)’s would lead to an improved estimator…

Filed under: Books, Statistics Tagged: Bernoulli, importance sampling, leave-one-out calibration, non-parametric kernel estimation, unbiased estimation, variance correction ]]>

Filed under: Books, Statistics Tagged: cross validated, Dirichlet distribution, LaTeX, marginalisation, order statistics, Peter Dirichlet, Stack Exchange, stamp ]]>

B¹⁰(p) ≤ 1/-e p log p

with the specificity that B¹⁰(p) is not testing the original hypothesis [problem] but a substitute where the null is the hypothesis that p is uniformly distributed, versus a non-parametric alternative that p is more concentrated near zero. This reminded me of our PNAS paper on the impact of summary statistics upon Bayes factors. And of some forgotten reference studying Bayesian inference based solely on the p-value… It is too bad I had to rush back to Paris, as this made me miss the last talks of this fantastic workshop centred on maybe the most important aspect of statistics!

Filed under: Statistics Tagged: Bayesian hypothesis testing, birthday problem, bounds, brain imaging, CRiSM, decision theory, E.T. Jaynes, England, fMRI, Genetics, Gregor Mendel, ISBA 2016, p-values, permutation tests, PNAS, podcast, psychology, University of Warwick, Zeeman building ]]>

*“The wilderness does not make you forget your normal life as much as it removes the distractions for proper remembering.” *J. Harrison

**O**ne of my favourite authors passed away earlier this year and I was not even aware of it! Jim Harrison died from a heart attack in Arizona on March 26. I read Legends of the Fall [for the first time] when I arrived in the US in 1987 and then other [if not all] novels like A good day to die or Wolf…

“Barring love, I’ll take my life in large doses alone: rivers, forests, fish, grouse, mountains. Dogs.”J. Harrison

What I liked in those novels was less the plot, which often is secondary—even though the Cervantesque story of the two guys trying to blow a dam in A good day to die is pure genius!—, than the depiction of the characters and their almost always bleak life, as well as the love of outdoors, in a northern Michigan that is at its heart undistinguishable from (eastern) Canada or central Finland. His tales told of eating and drinking, of womanising, fishing, and hunting, of failed promises and multiple capitulations, tales that are always bawdy and brimming with testosterone, but also with a gruff tenderness for those big hairy guys and their dogs. Especially their dogs. There is a lot of nostalgia seeping through these stories, a longing for a wild rural (almost feral) America that most people will never touch. Or even conceive. But expressed in a melancholic rather than reactionary way. In a superb prose that often sounded like a poem.

“I like grit, I like love and death, I am tired of irony…”J. Harrison

If anything, remembering those great novels makes me long for the most recent books of Harrison I have not [yet] read. Plus the non-fiction book The Raw and the Cooked.

Filed under: Statistics Tagged: A Good Day to Die, Arizona, Jim Harrison, Lake Michigan, Legends of the Fall, Upper Peninsula ]]>

Filed under: Kids, pictures, Travel, Wines Tagged: MIchelin starred restaurant, Parc de Sceaux, restaurant, sardines ]]>