## icefalls on Ben Nevis

Posted in Mountains, pictures, Travel with tags , , , , , , , on January 31, 2015 by xi'an

The seminar invitation to Edinburgh gave me the opportunity and the excuse for a quick dash to Fort William for a day of ice-climbing on Ben Nevis. The ice conditions were perfect but there was alas too much snowdrift to attempt Point Five Gully, one of the mythical routes on the Ben. (Last time, the ice was not in good conditions.) Instead, we did three pitches on three different routes, one iced rock-face near the CIC hut, the first pitch of Waterfall Gully on Carn Dearg Buttress, and the first pitch of The Curtain, again on Carn Dearg Buttress.

The most difficult climb was the first one, grading about V.5 in Scottish grade, maybe above that as the ice was rather rotten, forcing my guide Ali to place many screws. And forcing me to unscrew them! Then the difficulty got much lower, except for the V.5 start of the Waterfall, where I had to climb with hands an ice pillar as the ice-picks would not get a good grip. Breaking another large pillar in the process, fortunately mostly avoiding being hit. The final climb was quite easy, more of a snow steep slope than a true ice-climb. Too bad the second part of the route was blocked by two fellows who could not move! Anyway, it was another of those rare days on the ice, with enough choice to worry about sharing with other teams, and a terrific guide! And a reasonable day for Scotland with little snow, no rain, plenty of wind and not that cold (except when belaying!).

## icicles on the Ben

Posted in Mountains, pictures, Travel with tags , , , on January 25, 2015 by xi'an

## brief stop in Edinburgh

Posted in Mountains, pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , on January 24, 2015 by xi'an

Yesterday, I was all too briefly in Edinburgh for a few hours, to give a seminar in the School of Mathematics, on the random forests approach to ABC model choice (that was earlier rejected). (The slides are almost surely identical to those used at the NIPS workshop.) One interesting question at the end of the talk was on the potential bias in the posterior predictive expected loss, bias against some model from the collection of models being evaluated for selection. In the sense that the array of summaries used by the random forest could fail to capture features of a particular model and hence discriminate against it. While this is correct, there is no fundamental difference with implementing a posterior probability based on the same summaries. And the posterior predictive expected loss offers the advantage of testing, that is, for representative simulations from each model, of returning the corresponding model prediction error to highlight poor performances on some models. A further discussion over tea led me to ponder whether or not we could expand the use of random forests to Bayesian quantile regression. However, this would imply a monotonicity structure on a collection of random forests, which sounds daunting…

My stay in Edinburgh was quite brief as I drove to the Highlands after the seminar, heading to Fort William, Although the weather was rather ghastly, the traffic was fairly light and I managed to get there unscathed, without hitting any of the deer of Rannoch Mor (saw one dead by the side of the road though…) or the snow banks of the narrow roads along Loch Lubnaig. And, as usual, it still was a pleasant feeling to drive through those places associated with climbs and hikes, Crianlarich, Tyndrum, Bridge of Orchy, and Glencoe. And to get in town early enough to enjoy a quick dinner at The Grog & Gruel, reflecting I must have had half a dozen dinners there with friends (or not) over the years. And drinking a great heather ale to them!

## how many modes in a normal mixture?

Posted in Books, Kids, Statistics, University life with tags , , , , , , on January 7, 2015 by xi'an

An interesting question I spotted on Cross Validated today: How to tell if a mixture of Gaussians will be multimodal? Indeed, there is no known analytical condition on the parameters of a fully specified k-component mixture for the modes to number k or less than k… Googling around, I immediately came upon this webpage by Miguel Carrera-Perpinan, who studied the issue with Chris Williams when writing his PhD in Edinburgh. And upon this paper, which not only shows that

1. unidimensional Gaussian mixtures with k components have at most k modes;
2. unidimensional non-Gaussian mixtures with k components may have more than k modes;
3. multidimensional mixtures with k components may have more than k modes.

but also provides ways of finding all the modes. Ways which seem to reduce to using EM from a wide variety of starting points (an EM algorithm set in the sampling rather than in the parameter space since all parameters are set!). Maybe starting EM from each mean would be sufficient.  I still wonder if there are better ways, from letting the variances decrease down to zero until a local mode appear, to using some sort of simulated annealing…

Edit: Following comments, let me stress this is not a statistical issue in that the parameters of the mixture are set and known and there is no observation(s) from this mixture from which to estimate the number of modes. The mathematical problem is to determine how many local maxima there are for the function

$f(x)\,:\,x \longrightarrow \sum_{i=1}^k p_i \varphi(x;\mu_i,\sigma_i)$

## up North

Posted in pictures, Travel, University life with tags , , , , , on December 14, 2014 by xi'an

## Wien graffitis

Posted in Kids, pictures, Running, Travel with tags , , , , , on October 12, 2014 by xi'an

## Scottish polls…

Posted in pictures, Statistics, Travel with tags , , , , , , , , on September 11, 2014 by xi'an

As much as I love Scotland, or because of it, I would not dream of suggesting to Scots that one side of the referendum sounds better than the other. However, I am rather annoyed at the yoyo-like reactions to the successive polls about the result, because, just like during the US elections, each poll is analysed separately rather than being pooled with the earlier ones in a reasonable meta-analysis… Where is Nate Silver when we need him?!