## Snapshots from CRiSM workshop

Posted in Statistics, University life with tags , , , , , , , , on May 31, 2010 by xi'an

The workshop is a mix of theory, methodology, computational techniques and applications that makes it quite exciting. Although I already gave several versions of my talk in the past year, I still got interesting feedback, in particular a connection between our Savage-Dickey representation and bridge sampling. Among the interesting talks I attended, a few snapshots; both Jim Berger and Dongchu Sun presented new closed form expressions for effective numbers of parameters in complex linear models, Antonio Lijoi covered some mathematics of species estimation models [with some possible connections with Geoff Nicholls'  earlier talk on language classification], Chris Holmes exposed the advances he had made since Edinburgh (at least for those of us who attended both meetings), highlighting an interesting link with LDA, both Chris and Matthew Stephens considering direction selection for discrimination and clustering, Peter Müller talked about the analysis of a genetic pathway model represented as a graph, Robert Kohn zoomed through an adaptive particle MCMC algorithm where the likelihood was estimated (with the interesting side comment that what looks as an unbiased estimator from one perspective is also an auxiliary joint likelihood from another perspective) and David Spiegelhalter gave a both hilarious and thought-provoking talk on the “deeper uncertainty” that surrounds statistical models.

## Visit of an hedgehog

Posted in Kids, pictures with tags , on May 31, 2010 by xi'an

On Friday, a [visiting] friend of my kids pointed out to us an hedgehog crossing our lawn. We watched it for a while meandering in the grass before it vanished through the fence. The same (?) hedgehog came back on Saturday and it was quite unfazed by my presence, so I took a few pictures while it was visiting my rhubarb patch…

I am quite amazed that hedgehogs manage to survive on the very small patches of “nature” remaining around our densely urbanised suburb… (A wild boar made it to the local park a few years ago but this is another scale!) Two years ago, there was actually a family nesting into a pile of leaves but they did not show up last summer and early this year I saw one hedgehog killed on the nearby road. This could have been the mother of the current one… Which I hope will remain in the garden for a long while!

## Talk at CRiSM

Posted in R, Statistics, University life with tags , , , , , , , , on May 30, 2010 by xi'an

This is the talk I am giving at the workshop on model uncertainty organised by the Centre for Research in Statistical Methodology (CRiSM) at the University of Warwick, on May 30-June 1. Careful readers will notice there is not much difference with my previous talk on the topic, as I only included the Savage-Dickey slides from the talk in San Antonio!

## a DIY lesson

Posted in Kids with tags , , , on May 30, 2010 by xi'an

Last morning, I biked with my daughter to the local market as she was looking for a cloth bracelet that is seemingly highly in fashion at her school! The first shop we came upon was selling the thing at an outrageous price and she decided this was not worth the expense. So we walked around till we came by the only haberdasher’s shop in the neighbourhood and I suggested she took a look inside, just in case. As it happened, the haberdasher had got wind of the school fashion and she was selling appropriate pieces of cloth along with the compulsory trinkets! In the end, my daughter got enough material to make eleven of those (transient) bracelets at a cost lower than the original price. A good Saturday lesson in practical economics. (And a fairly unique opportunity for using the word haberdasher which has always sounded somehow military to me, suggesting a type of fighting corps, maybe because of the association with halberd! Anyway, it sounds much more martial than the French mercerie… And its Norman translation mercery.)

## La Robinsonnaise [5k]

Posted in Running, Travel with tags , , , , , on May 29, 2010 by xi'an

Tonight, as I am flying to Birmingham for the CRiSM workshop on Model uncertainty, I will miss my local 5k, La Robinsonnaise, for the first time in a long while. Last year saw the beginning of my sciatica symptoms, while the year before that led to two broken fingers due to a fall during the recovery run… Still, I will miss it as it would have been good practice for the 10k I am running on Thursday afternoon in Vincennes. So I went for a faster run this morning, running the 3k loop in the local park in 11:46 then the second one in 11:22, which is ok given the absence of split training this year. (From what I remember, the best 3k in the 3k-1k-3k split should be around 11:05…) Another disappointment I came upon a few days ago when running with my friends of Insee Paris Club is that I have to wait another year to join the V2 category, as the rules have changed… This obviously means less chances of ending in a good position for the half-marathon in Argentan!

## Savage-Dickey revised

Posted in Statistics with tags , , , , on May 29, 2010 by xi'an

We have at last re-submitted (and rearXived, but only to appear on Monday!) our paper on the Savage-Dickey paradox to the Electronic Journal of Statistics (after wasting a few weeks doing nothing!). The revision was quite easy to write, especially because the comments applied to an earlier version of the paper I had submitted by mistake and  theyrequested examples thatactually  were  in the latest version! The comments were in any case quite supportive, although some hinted at a partial misunderstanding with the nature of the “paradox”. I am afraid the measure-theoretic difficulty with this Savage-Dickey paradox will not vanish once the paper is published.

## A repulsive random walk

Posted in R, Statistics with tags , , , , on May 28, 2010 by xi'an

Matt Asher posted an R experiment on R-bloggers yesterday simulating the random walk

$x_{t+1} = x_t + \varepsilon_t / x_t$

which has the property of avoiding zero by quickly switching to a large value as soon as $x_t$ is small. He was then wondering about the “convergence” of the random walk given that it moves very little once $x_t$ is large enough. The values he found for various horizons t seemed to indicate a stable regime.

I reran the same experiment as Matt in a Monte Carlo perspective, using the R program

resu=matrix(0,ncol=100,nrow=25)
sampl=rnorm(100)
for (i in 1:25){
for (t in 2^(i-1):2^i) sampl=sampl+rnorm(100)/sampl
resu[i,]=sampl
}
boxplot(as.data.frame(t(abs(resu))),name=as.character(1:25),col="wheat3")

The outcome of this R code plotted above shows that the range and the average of the 100 replications is increasing with t. This behaviour indicates a transient behaviour of the Markov chain, which almost surely goes to infinity and never comes back (because at infinity the variance is zero). Another indication for transience is shown by the fact that $x_t$ comes back to the interval (-1,1) with probability $\Phi(-|x_t|)$, a probability which goes to zero with $x_t$. As suggested to me by Randal Douc, this transience can be established rigorously by considering

$x_{t+1}^2 = x_t^2 + 2\epsilon_t + \epsilon_t^2/x_t^2 > x_t^2 + 2\epsilon_t>2\sum_{i=1}^t \epsilon_t$

which is thus bounded from below by a null recurrent process, which almost surely goes to infinity. Therefore the above Markov chain cannot have a stationary distribution or even a stationary measure: it almost surely goes to (plus or minus) infinity.