**W**hile I found the latest Rankin’s Rebus novels a wee bit disappointing, this latest installment in the stories of the Edinburghian ex-detective is a true pleasure! Maybe because it takes the pretext of a “cold case” suddenly resurfacing to bring back to life characters met in earlier novels of the series. And the borderline practice of DI Rebus himself. Which should matter less at a stage when Rebus has been retired for 10 years (I could not believe it had been that long!, but I feel like I followed Rebus for most of his carreer…) The plot is quite strong with none of the last minute revelations found in some earlier volumes, with a secondary plot that is much more modern and poignant. I also suspect some of the new characters will reappear in the next books, as well as the consequences of a looming Brexit [pushed by a loony PM] on the Scottish underworld… (No,. I do not mean ~~Torys~~Tories!)

## Archive for Scotland

## in a house of lies [book review]

Posted in Books, Travel with tags Brexit, detective story, Edinburgh, Glasgow, Ian Rankin, PM, Rebus, retirement, Scotland on August 7, 2019 by xi'an## thermodynamic integration plus temperings

Posted in Statistics, Travel, University life with tags Craigh Meagaidh, Edinburgh, exchange algorithm, foot and mouth epidemics, Galaxy, ICMS, intractable constant, marginal likelihood, radial speed, Scotland, simulated tempering, temperature schedule, thermodynamic integration on July 30, 2019 by xi'an**B**iljana Stojkova and David Campbel recently arXived a paper on the used of parallel simulated tempering for thermodynamic integration towards producing estimates of marginal likelihoods. Resulting into a rather unwieldy acronym of PT-STWNC for “Parallel Tempering – Simulated Tempering Without Normalizing Constants”. Remember that parallel tempering runs T chains in parallel for T different powers of the likelihood (from 0 to 1), potentially swapping chain values at each iteration. Simulated tempering monitors a single chain that explores both the parameter space and the temperature range. Requiring a prior on the temperature. Whose optimal if unrealistic choice was found by Geyer and Thomson (1995) to be proportional to the inverse (and unknown) normalising constant (albeit over a finite set of temperatures). Proposing the new temperature instead via a random walk, the Metropolis within Gibbs update of the temperature τ then involves normalising constants.

*“This approach is explored as proof of concept and not in a general sense because the precision of the approximation depends on the quality of the interpolator which in turn will be impacted by smoothness and continuity of the manifold, properties which are difficult to characterize or guarantee given the multi-modal nature of the likelihoods.”*

To bypass this issue, the authors pick for their (formal) prior on the temperature τ, a prior such that the profile posterior distribution on τ is constant, i.e. the joint distribution at τ and at the mode [of the conditional posterior distribution of the parameter] is constant. This choice makes for a closed form prior, provided this mode of the tempered posterior can *de facto* be computed for each value of τ. (However it is unclear to me why the exact mode would need to be used.) The resulting Metropolis ratio becomes independent of the normalising constants. The final version of the algorithm runs an extra exchange step on both this simulated tempering version and the untempered version, i.e., the original unnormalised posterior. For the marginal likelihood, thermodynamic integration is invoked, following Friel and Pettitt (2008), using simulated tempering samples of (θ,τ) pairs (associated instead with the above constant profile posterior) and simple Riemann integration of the expected log posterior. The paper stresses the gain due to a continuous temperature scale, as it “removes the need for optimal temperature discretization schedule.” The method is applied to the Glaxy (mixture) dataset in order to compare it with the earlier approach of Friel and Pettitt (2008), resulting in (a) a selection of the mixture with five components and (b) much more variability between the estimated marginal likelihoods for different numbers of components than in the earlier approach (where the estimates hardly move with k). And (c) a trimodal distribution on the means [and unimodal on the variances]. This example is however hard to interpret, since there are many contradicting interpretations for the various numbers of components in the model. (I recall Radford Neal giving an impromptu talks at an ICMS workshop in Edinburgh in 2001 to warn us we should not use the dataset without a clear(er) understanding of the astrophysics behind. If I remember well he was excluded all low values for the number of components as being inappropriate…. I also remember taking two days off with Peter Green to go climbing Craigh Meagaidh, as the only authorised climbing place around during the foot-and-mouth epidemics.) In conclusion, after presumably too light a read *(I did not referee the paper!),* it remains unclear to me why the combination of the various tempering schemes is bringing a noticeable improvement over the existing. At a given computational cost. As the temperature distribution does not seem to favour spending time in the regions where the target is most quickly changing. As such the algorithm rather appears as a special form of exchange algorithm.

## Bayesian econometrics in St. Andrews

Posted in Mountains, pictures, Statistics, Travel, University life with tags Bayesian econometrics, call for papers, conference, ESOBE, ISBA, Scotland, Skye, St Andrews, sunset, University of St Andrews, young Bayesians on April 8, 2019 by xi'an**A**call I received for the incoming 2019 edition of the European Seminar on Bayesian Econometrics (ESOBE), sponsored by the EFaB section of ISBA, which is going to be held at the University of St Andrews in Scotland on Monday 2 and Tuesday 3 September, 2019. I have attended an earlier edition in Venezia and enjoyed it very much. Plus, summer in Scotland…, where else?! Submission of papers is still open:

We aim to have a balance of keynotes from both statistics and econometrics, in order to stimulate submissions from statisticians working on Bayesian methodology or applications in economics/finance. We particularly welcome submissions from young Bayesians (PhDs, PostDocs, assistant professors — EFaB funds a “young researcher session” with up to $500 per speaker).

## avalanche on the Ben…

Posted in Statistics with tags Ben Nevis, Glencoe, Glencoe Mountain Rescue Team, helicopter rescue, Highlands, mountain climbing, mountain rescue, Scotland on March 12, 2019 by xi'an## Fate & Fortune [book review]

Posted in Books, Travel with tags caitch, Church of Scotland, Edinburgh, hue & cry, real tennis, Scotland, Shirley McKay, St. Andrew on February 10, 2019 by xi'an**A**fter enjoying very much the first book, Hue & Cry, in the Hew Cullan series by Shirley McKay, I bought the following ones and read Fate & Fortune over the vacation break. If anything, I enjoyed this one even more, as it disclosed other aspects of 16th Century Scotland, still with the oppressive domination of the Kirk, the highly puritan Church of Scotland, over all aspects of everyday life, but also a more rational form of Law, plus the first instances of caitch, imported from France jeu de paume. And the medical approach of the time against an epidemics of syphilis. And the dangerous life of printers at the time, always in danger of arrest and worse. As usual with historical whodunits, it is hard to guess what is genuinely from 1580’s and what has been imported from the present era, but this is a most pleasant (light and short) book to read!