**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 Edinburgh

## 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.

## 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!

## hue & cry [book review]

Posted in Statistics with tags book review, Church of Scotland, Edinburgh, hue & cry, Scotland, St. Andrew, witchery on December 8, 2018 by xi'an**W**hile visiting the Blackwell’s bookstore by the University of Edinburgh last June, I spotted this historical whodunit in the local interest section. Hue & Cry by Shirley McKay. It stayed on a to-read pile by my bed until a few weeks ago when I started reading it and got more and more engrossed in the story. While the style is not always at its best and the crime aspects are somewhat thin, I find the description of the Scottish society of the time (1570’s) fascinating (and hopefully accurate), especially the absolute dominion of the local Church (Kirk) on every aspect of life and the helplessness of women always under the threat of witchcraft accusations. Which could end up with the death penalty, as in thousands of cases. The book reminds me to some extent of the early Susanna Gregory’s books in that it also involves scholars, teaching well-off students with limited intellectual abilities, while bright but poorer students have to work for the college to make up for their lack of funds. As indicated above, the criminal part is less interesting as the main investigator unfolds the complicated plot without much of a hint. And convinces the juries rather too easily in my opinion. An overall fine novel, nonetheless!

## the naming of the Dead [book review]

Posted in Statistics with tags Auchterader, book review, Edinburgh, Edinburgh Castle, G8, G8 meeting, George W Bush, Gleneagles, Ian Rankin, ISBA 2018, Rebus, Scotland, Scottish crime novel, the naming of the Dead on July 21, 2018 by xi'an**W**hen leaving for ISBA 2018 in Edinburgh, I picked a Rebus book in my bookshelf, book that happened to be The Naming of the Dead, which was published in 2006 and takes place in 2005, during the week of the G8 summit in Scotland and of the London Underground bombings. Quite a major week in recent British history! But also for Rebus and his colleague Siobhan Clarke, who investigate a sacrificial murder close, too close, to the location of the G8 meeting and as a result collide with superiors, secret services, protesters, politicians, and executives, including a brush with Bush ending up with his bike accident at Gleneagles, and ending up with both of them suspended from the force. But more than this close connection with true events in and around Edinburgh, the book is a masterpiece, maybe Rankin’s best, because of the depiction of the characters, who have even more depth and dimensions than in the other novels. And for the analysis of the events of that week. Having been in Edinburgh at the time I started re-reading the book also made the description of the city much more vivid and realistic, as I could locate and sometimes remember some places. (The conclusion of some subplots may be less realistic than I would like them to be, but this is of very minor relevance.)

## ISBA 18 tidbits

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags ABC, ABC in Edinburgh, Bayesian inference, coreset, deep learning, Edinburgh, empirical likelihood, Ironman Edinburgh, ISBA 2018, kilt, marginal likelihood, misspecification, misspecified model, non-local priors, non-parametrics, PAC-Bayesian, posters, Scotland on July 2, 2018 by xi'an**A**mong a continuous sequence of appealing sessions at this ISBA 2018 meeting [says a member of the scientific committee!], I happened to attend two talks [with a wee bit of overlap] by Sid Chib in two consecutive sessions, because his co-author Ana Simoni (CREST) was unfortunately sick. Their work was about models defined by a collection of moment conditions, as often happens in econometrics, developed in a recent JASA paper by Chib, Shin, and Simoni (2017). With an extension about moving to defining conditional expectations by use of a functional basis. The main approach relies on exponentially tilted empirical likelihoods, which reminded me of the empirical likelihood [BCel] implementation we ran with Kerrie Mengersen and Pierre Pudlo a few years ago. As a substitute to ABC. This problematic made me wonder on how much Bayesian the estimating equation concept is, as it should somewhat involve a nonparametric prior under the moment constraints.

Note that Sid’s [talks and] papers are disconnected from ABC, as everything comes in closed form, apart from the empirical likelihood derivation, as we actually found in our own work!, but this could become a substitute model for ABC uses. For instance, identifying the parameter θ of the model by identifying equations. Would that impose too much input from the modeller? I figure I came with this notion mostly because of the emphasis on proxy models the previous day at ABC in ‘burgh! Another connected item of interest in the work is the possibility of accounting for misspecification of these moment conditions by introducing a vector of errors with a spike & slab distribution, although I am not sure this is 100% necessary without getting further into the paper(s) [blame conference pressure on my time].

Another highlight was attending a fantastic poster session Monday night on computational methods except I would have needed four more hours to get through every and all posters. This new version of ISBA has split the posters between two sites (great) and themes (not so great!), while I would have preferred more sites covering all themes over all nights, to lower the noise (still bearable this year) and to increase the possibility to check all posters of interest in a particular theme…

Mentioning as well a great talk by Dan Roy about assessing deep learning performances by what he calls non-vacuous error bounds. Namely, through PAC-Bayesian bounds. One major comment of his was about deep learning models being much more non-parametric (number of parameters rising with number of observations) than parametric models, meaning that generative adversarial constructs as the one I discussed a few days ago may face a fundamental difficulty as models are taken at face value there.

On closed-form solutions, a closed-form Bayes factor for component selection in mixture models by Fũqene, Steel and Rossell that resemble the Savage-Dickey version, without the measure theoretic difficulties. But with non-local priors. And closed-form conjugate priors for the probit regression model, using unified skew-normal priors, as exhibited by Daniele Durante. Which are product of Normal cdfs and pdfs, and which allow for closed form marginal likelihoods and marginal posteriors as well. (The approach is not exactly conjugate as the prior and the posterior are not in the same family.)

And on the final session I attended, there were two talks on scalable MCMC, one on coresets, which will require some time and effort to assimilate, by Trevor Campbell and Tamara Broderick, and another one using Poisson subsampling. By Matias Quiroz and co-authors. Which did not completely convinced me (but this was the end of a long day…)

All in all, this has been a great edition of the ISBA meetings, if quite intense due to a non-stop schedule, with a very efficient organisation that made parallel sessions manageable and poster sessions back to a reasonable scale [although I did not once manage to cross the street to the other session]. Being in unreasonably sunny Edinburgh helped a lot obviously! I am a wee bit disappointed that no one else follows my call to wear a kilt, but I had low expectations to start with… And too bad I missed the Ironman 70.3 Edinburgh by one day!