Archive for Loch Lomond

the buzz about nuzz

Posted in Books, Mountains, pictures, Statistics with tags , , , , , , , , , , , , , on April 6, 2020 by xi'an

“…expensive in these terms, as for each root, Λ(x(s),v) (at the cost of one epoch) has to be evaluated for each root finding iteration, for each node of the numerical integral

When using the ZigZag sampler, the main (?) difficulty is in producing velocity switch as the switches are produced as interarrival times of an inhomogeneous Poisson process. When the rate of this process cannot be integrated out in an analytical manner, the only generic approach I know is in using Poisson thinning, obtained by finding an integrable upper bound on this rate, generating from this new process and subsampling. Finding the bound is however far from straightforward and may anyway result in an inefficient sampler. This new paper by Simon Cotter, Thomas House and Filippo Pagani makes several proposals to simplify this simulation, Nuzz standing for numerical ZigZag. Even better (!), their approach is based on what they call the Sellke construction, with Tom Sellke being a probabilist and statistician at Purdue University (trivia: whom I met when spending a postdoctoral year there in 1987-1988) who also wrote a fundamental paper on the opposition between Bayes factors and p-values with Jim Berger.

“We chose as a measure of algorithm performance the largest Kolmogorov-Smirnov (KS) distance between the MCMC sample and true distribution amongst all the marginal distributions.”

The practical trick is rather straightforward in that it sums up as the exponentiation of the inverse cdf method, completed with a numerical resolution of the inversion. Based on the QAGS (Quadrature Adaptive Gauss-Kronrod Singularities) integration routine. In order to save time Kingman’s superposition trick only requires one inversion rather than d, the dimension of the variable of interest. This nuzzled version of ZIgZag can furthermore be interpreted as a PDMP per se. Except that it retains a numerical error, whose impact on convergence is analysed in the paper. In terms of Wasserstein distance between the invariant measures. The paper concludes with a numerical comparison between Nuzz and random walk Metropolis-Hastings, HMC, and manifold MALA, using the number of evaluations of the likelihood as a measure of time requirement. Tuning for Nuzz is described, but not for the competition. Rather dramatically the Nuzz algorithm performs worse than this competition when counting one epoch for each likelihood computation and better when counting one epoch for each integral inversion. Which amounts to perfect inversion, unsurprisingly. As a final remark, all models are more or less Normal, with very smooth level sets, maybe not an ideal range


from down-under, Lake Menteith upside-down

Posted in Books, R, Statistics with tags , , , , on January 23, 2013 by xi'an

Lake Menteith Landsat image, as printed in Bayesian Core (2007)The dataset used in Bayesian Core for the chapter on image processing is a Landsat picture of Lake of Menteith in Scotland (close to Loch Lomond). (Yes, Lake of Menteith, not Loch Menteith!) Here is the image produced in the book. I just got an email from Matt Moores at QUT that the image is both rotated and flipped:

The image of Lake Mentieth in figure 8.6 of Bayesian Core is upside-down and back-to-front, so to speak. Also, I recently read a paper by Lionel Cucala & J-M Marin that has the same error.

This is due to the difference between matrix indices and image coordinates: matrices in R are indexed by [row,column] but image coordinates are [x,y]. Also, y=1 is the first row of the matrix, but the bottom row of pixels in an image.

Only a one line change to the R code is required to display the image in the correct orientation:


As can be checked on Googlemap, the picture is indeed rotated by a -90⁰ angle and the transpose correction does the job!

Another beautiful if hellish trip

Posted in Mountains, pictures, Travel, University life with tags , , , , , on June 2, 2011 by xi'an

Sounds like my Scottish trips are all doomed the same way: once again, the airline (FlyBe) managed to loose my luggage, even though this time I had it as carry-on luggage! Since the plane was a very small propeler plane, the [small climbing] backpack (containing among other things my hiking clothes!, if not my laptop) was taken by the flight attendant in Paris, but did not show up at the bottom of the stairs in Glasgow. I lost another hour at the Glasgow airport with the (kind) luggage people, all for nothing, and I very much feared the bag would never reappear as it was not a registered item of luggage! It actually showed up at the hotel the day after around midnight, just before my planned hike.

In addition, the flight itself was terrible with a 25 minute stop in Cardiff, Wales, where we had to rush through custom and security. (This is also where someone dropped my backpack!) And a plane full of screaming kids back returning from Disneyland Paris… Maybe should I consider using the train next time! (And then the internet at the hotel was not working at all and it would not have worked anyway as they used an antiquated modem plug rather than wireless or the standard ethernet plug!)

On the bright side, an extra-reward of the trip was indeed that I managed to climb Ben Lomond in the morning before my flight, thanks to Adrian Bowman who kindly took me there despite having to wake up at a particularly ungodly hour! We had great views of Loch Lomond before entering a cloud that would not lift for the rest of the walk, but it did not really rain and the weather was rather mild, except for sudden gusts of wind. The way down via Ptarmingan Ridge was a very nice drop towards Loch Lomond with highly rewarding views once out of the cloud. Given the popularity of Ben Lomond, the trail is also well-maintained, which means we managed to keep dry foots all the way around. It was thus quite nice to spend a few hours (about 3:30 for the round trip) in from of the Arrochar Alps before flying back to Paris, having never been on Ben Lomond before…

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