## Archive for Edinburgh

## Bayes plaque

Posted in Books, pictures, Statistics, Travel, University life with tags Bayes theorem, Edinburgh, FRS, plaque, Royal Society, Scotland, Thomas Bayes, University of Edinburgh on November 22, 2019 by xi'an## at the centre of Bayes

Posted in Mountains, pictures, Statistics, Travel, University life with tags 2019 Education Buildings Scotland Awards, Arthur's Seat, Bayes Café, Bayes Centre, Brown University, ECERM, Edinburgh, Holyrood Park, ICMS, jatp, Maxwell Institute Colloquium, Maxwell Institute Graduate School, Scotland, Scottish sun, seminar, Thomas Bayes, University of Edinburgh on October 14, 2019 by xi'an## HW AMS & EPSRC MAG-MIGS CDT seminar

Posted in Statistics with tags ABC convergence, Bayes Centre, Centre for Doctoral Training, Edinburgh, EPSRC, Heriot-Watt University, Maxwell Institute Graduate School, misspecification, Scotland, University of Edinburgh on October 10, 2019 by xi'an**S**ome explanation for all these acronyms! I am giving a Actuarial Mathematics & Statistics (AMS) seminar at Heriot-Watt (HW) University, in Edinburgh, tomorow. But in the (new) Bayes Centre, at the University of Edinburgh, rather than on the campus of Heriot-Watt, as this is also the launching day of the Centre for Doctoral Training (CDT) on Mathematical Modelling, Analysis, & Computation (MAG) shared between Heriot-Watt, and the University of Edinburgh, funded by the EPSRC and located in the Maxwell Institute Graduate School (MIGS) in its Bayes Centre. My talk will be on ABC convergence and misspecification.

## 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**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!)

## 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.