**I**n my office hangs this poster of Adam Ondra climbing at sunset an impressive overhang with a little Czech town at the foot of the cliff, already in the shade. Impressive because of the view and of the climb which at 7c is a whole grade (and then some) beyond my reach. But now Ondra has managed to climb the first 9c in the world, which is universes beyond the impressive and beyond the fathomable, with passages only manageable feet first. Which actually makes a lot of sense, the way he explains it. The route is currently called *Project Hard *and is located* *in Hanshelleren Cave, Flatanger, Norway.

## Archive for extremes

## Adam Ondra completes a first 9c

Posted in Kids, Mountains, pictures with tags 9c, Adam Ondra, extremes, Flatanger, Hanshelleren Cave, Norway, sport climbing on September 30, 2017 by xi'an## Texan black swan

Posted in Books, pictures with tags devil, extremes, flood, Harvey, Houston, Le Monde, Nassim Taleb, Texas, The Black Swan on September 12, 2017 by xi'an

“Un événement improbable aux conséquences d’autant plus désastreuses que l’on ne s’y est pas préparé.”

**T**his weekend, there was a short article in Le Monde about the Harvey storm as a Texan illustration of Taleb’s black swan. An analysis that would imply every extreme event like this “once-in-a-thousand year” event (?) can be called a black swan… “An improbable event with catastrophic consequences, the more because it had not been provisioned”, as the above quote translates. Ironically, there is another article in the same journal, about the catastrophe being “ordinary” and “not unexpected”! While such massive floods are indeed impacting a huge number of people and companies, because the storm happened to pour an unusual amount of rain right on top of Houston, they indeed remain within the predictable and not so improbable in terms of the amount of water deposited in the area and in terms of damages, given the amount and style of construction over flood plains. For instance, Houston is less than 50 feet above sea level, has fairly old drainage and pipe systems, and lacks a zoning code. With mostly one or two-story high buildings rather than higher rises. (Incidentally, I appreciated the juxtaposition of the article with the add for Le Monde des Religions and its picture of a devilesque black goat!)

## Statistics month in Marseilles (CIRM)

Posted in Books, Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags Bayesian Essentials with R, Bayesian statistics, bouillabaisse, calanques, Cassis, CIRM, CNRS, copulas, extremes, France, machine learning, Marseille, minicourse, SMF, stochastic processes on June 24, 2015 by xi'an**N**ext February, the fabulous Centre International de Recherche en Mathématiques (CIRM) in Marseilles, France, will hold a Statistics month, with the following programme over five weeks

- 1 – 6 February, 2016 Learning
- 8 – 12 February, 2016 Mathématical statistics
- 15 – 19 February, 2016 Processes
- 22 – 26 February, 2016 Extremes, Copulas and Actuarial Science
- 29 February – 4 March, 2016 Bayesian statistics and algorithms

Each week will see minicourses of a few hours (2-3) and advanced talks, leaving time for interactions and collaborations. (I will give one of those minicourses on Bayesian foundations.) The scientific organisers of the B’ week are Gilles Celeux and Nicolas Chopin.

The CIRM is a wonderful meeting place, in the mountains between Marseilles and Cassis, with many trails to walk and run, and hundreds of fantastic climbing routes in the Calanques at all levels. (In February, the sea is too cold to contemplate swimming. The good side is that it is not too warm to climb and the risk of bush fire is very low!) We stayed there with Jean-Michel Marin a few years ago when preparing Bayesian Essentials. The maths and stats library is well-provided, with permanent access for quiet working sessions. This is the French version of the equally fantastic German Mathematik Forschungsinstitut Oberwolfach. There will be financial support available from the supporting societies and research bodies, at least for young participants and the costs if any are low, for excellent food and excellent lodging. Definitely not a scam conference!

## dynamic mixtures [at NBBC15]

Posted in R, Statistics with tags Arnoldo Frigessi, component of a mixture, cross validated, dynamic mixture, extremes, Havard Rue, NBBC15 conference, O-Bayes 2015, Pareto distribution, R, Reykjavik, Valencia conferences, Weibull distribution on June 18, 2015 by xi'an**A** funny coincidence: as I was sitting next to Arnoldo Frigessi at the NBBC15 conference, I came upon a new question on Cross Validated about a dynamic mixture model he had developed in 2002 with Olga Haug and Håvård Rue [whom I also saw last week in Valencià]. The dynamic mixture model they proposed replaces the standard weights in the mixture with cumulative distribution functions, hence the term *dynamic*. Here is the version used in their paper (x>0)

where f is a Weibull density, g a generalised Pareto density, and w is the cdf of a Cauchy distribution [all distributions being endowed with standard parameters]. While the above object is *not* a mixture of a generalised Pareto and of a Weibull distributions (instead, it is a mixture of two non-standard distributions with unknown weights), it is close to the Weibull when x is near zero and ends up with the Pareto tail (when x is large). The question was about simulating from this distribution and, while an answer was in the paper, I replied on Cross Validated with an alternative accept-reject proposal and with a somewhat (if mildly) non-standard MCMC implementation enjoying a much higher acceptance rate and the same fit.

## MCMSki IV [day 2.5]

Posted in Mountains, pictures, Statistics, University life with tags ABC, AMIS, extremes, parallelisation, poster session, raclette, SNPs, sticky Metropolis, synthetic likelihood, warhammer on January 8, 2014 by xi'an**D**espite a good rest during the ski break, my cold did not get away (no magic left in this world!) and I thus had a low attention span to attend the *Bayesian statistics and Population genetics* session: while Jukka Corander mentioned the improvement brought by our AMIS algorithm, I had difficulties getting the nature of the model, if only because he used a blackboard-like font that made math symbols too tiny to read. (Nice fonts, otherwise!), Daniel Lawson (of vomiting Warhammer fame!) talked about the alluring notion of a statistical emulator, and Barbara Engelhardt talked about variable selection in a SNP setting. I did not get a feeling on how handling ten millions of SNPs was possible in towards a variable selection goal. My final session of the day was actually “my” invited session on ABC methods, where Richard Everitt presented a way of mixing exact approximation with ABC and synthetic likelihood (Wood, *Nature*) approximations. The resulting MAVIS algorithm is not out yet. The second speaker was Ollie Ratman, who spoke on his accurate ABC that I have discussed many times here. And Jean-Michel Marin managed to drive from Montpelier, just in time to deliver his talk on our various explorations of the ABC model choice problem.

**A**fter a quick raclette at “home”, we headed back to the second poster session, where I had enough of a clear mind and not too much of a headache (!) to have several interesting discussions, incl. a new parallelisation suggested by Ben Calderhead, the sticky Metropolis algorithm of Luca Martino, the airport management video of Jegar Pitchforth, the mixture of Dirichlet distributions for extremes by Anne Sabourin, not mentioning posters from Warwick or Paris. At the end of the evening I walked back to my apartment with the Blossom skis we had brought in the morning to attract registrations for the ski race: not enough to make up for the amount charged by the ski school. Too bad, especially given Anto’s efforts to get this amazing sponsoring!

## Good size swans and turkeys

Posted in Books, Statistics with tags extremes, Pareto, prediction, tails, The Black Swan on February 24, 2009 by xi'an**I**n connection with ** The Black Swan**, Nassim Taleb wrote a small essay called

**on The Edge. I found it much more pleasant to read than the book because (a) it directly focus on the difficulty of dealing with fat tail distributions and the prediction of extreme events, and (b) it is delivered in a much more serene tone than the book (imagine, just the single remark about the Frenchs!). The text contains insights on loss functions and inverse problems which, even though they are a bit vague, do mostly make sense. As for**

*The Fourth Quadrant***, I deplore (a) the underlying determinism of the author, which still seems to believe in an unknown (and possibly unachievable) model that would rule the phenomenon under study and (b) the lack of temporal perspective and of the possibility of modelling jumps as changepoints, i.e. model shifts. Time series have no reason to be stationary, the less so the more they depend on all kinds of exogeneous factors. I actually agree with Taleb that, if there is no information about the form of the tails of the distribution corresponding to the phenomenon under study—assuming there does exist a distribution—, estimating the shape of this tail from the raw data is impossible.**

*The Black Swan***T**he essay is followed by a technical appendix that expands on fat tails, but not so deeply as to be extremely interesting. A surprising side note is that Taleb seems to associate stochastic volatility with mixtures of Gaussians. In my personal book of models, stochastic volatility is a noisy observation of the exponential of a random walk, something likethus with much higher variation (and possibly no moments). To state that Student’s t distributions are more variable than stochastic volatility models is therefore unusual… There is also an analysis over a bizillion datasets of the insanity of computing kurtosis when the underlying distribution may not have even a second moment. I could not agree more: trying to summarise fat tail distributions by their four first moments does not make sense, even though it may sell well. The last part of the appendix shows the equal lack of stability of estimates of the tail indexwhich again is not a surprising phenomenon: if the tail bound K is too low, it may be that the power law has not yet quicked in while, if it is too large, then we always end up with not enough data. The picture shows how the estimate widely varies with K around its theoretical value for the log-normal and three Pareto distributions, based on a million simulations. (And this is under the same assumption of stationarity as above.) So I am not sure what the message is there. (As an aside, there seems to be a mistake in the tail expectation: it should be

if the density decreases inIt is correct whenis the tail power of the cdf.)