Archive for ellipsoid

a (sunny, crisp) day at ICSDS 2025

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on December 19, 2025 by xi'an

While my first day at ICSDS 2025 was somewhat hectic, having realised late the night before that I was giving a talk!—I had forgotten I had submitted a title at registration time and never received any communication from the organisers, including (or excluding) a request for an abstract. I thus hastily updated my November talk in Sevilla for my December talk in Sevilla! but paid less attention than needed to the sessions I attended—, Wednesday was more peaceful—esp. after a 16K run along the Guadalquivir—and I engaged into two great Bayesian learning sessions, one that seemed designed for me!, involving my (40y long friend) Ed George on his latest result on proper prior minimaxity and shrinkage, with our late friend Bill Strawderman as a co-author since they worked on the problem prior to Bill’s demise, Charles Margossian on variational inference preserving some symmetries in the target and hence keeping the same statistics, with elliptically symmetric families, and Fletcher Christensen on DIC for some mixed models, with references to our “DIC’s eights” paper (but still picking one version of DIC in the end!)

The second session was on prediction learning!—with me as the chair, as I realized one minute before! AI !—with (my friend) Veronika Rockova using AI predictions as a prior predictive and connecting them with Bayesian nonparametrics, Kenyon Ng (who visited me last Spring) on a similar approach using pretrained transformers like TabPFN and martingale posterior inference, Lorenzo Cappello in a generalisation of martingale prediction and Andrea Ghiglietti on the mathematics of an involved urn system.


The afternoon session was a plenary talk by Daniela Witten in the magnificent building of the Real Fabrica de Tabacos, but the room was unfortunately too small for the audience and I could not enter. Hopefully her talk will have a significant intersection with the CRiSM colloquium she delivers in Warwick late January. I thus walked around the old town till the following poster session, held in the Real Fabrica courtyard, under the sun. As I got involved into a deep discussion of the relevance of mirror meetings (which I defend!) versus the dangers on principal (parent) conferences (which can be mitigated by the mirror conference participants registering, to some extent, for the principle one)—more to come on the ‘Og and in the ISBA Bulletin!—, I did not peruse the available posters, sorry…

And, by the way, the conference organisers also revealed the location of ICSDS 2026 which is Croatia, my first bet! In the city of Split we visited in 2023.

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reciprocal importance sampling

Posted in Books, pictures, Statistics with tags , , , , , , , , , on May 30, 2023 by xi'an

In a recent arXival, Metodiev et al. (including my friend Adrian Raftery, who is spending the academic year in Paris) proposed a new version of reciprocal importance sampling, expanding the proposal we made with Darren Wraith (2009) of using a Uniform over an HPD region. It is called THAMES, hence the picture (of London, not Paris!), for truncated harmonic mean estimator.

“…[Robert and Wraith (2009)] method has not yet been fully developed for realistic, higher-dimensional situations. For example, we know of no simple way to compute the volume of the convex hull of a set of points in higher dimensions.”

They suggest replacing the convex hull of the HPD points with an ellipsoid ϒ derived from a Normal distribution centred at the highest of the HPD points, whose covariance matrix is estimated from the whole (?) posterior sample. Which is somewhat surprising in that this ellipsoid may as well included low probability regions when the posterior is multimodal. For instance, the estimator is biased when the posterior cancels on parts of ϒ. And with an unclear fate for the finiteness of its variance, depending on how fast the posterior gets to zero on these parts.

The central feature of the paper is selecting the radius of the ellipse that minimises the variance of the (counter) evidence. Under asymptotic normality of the posterior. This radius roughly corresponds to our HPD region in that 50% of the sample stands within. The authors also notice that separate samples should be used to estimate the ellipse and to estimate the evidence. And that a correction is necessary when the posterior support is restricted. (Examples do not include multimodal targets, apparently.)

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Another slice

Posted in Statistics with tags , , , , on January 7, 2010 by xi'an

No this is not yet another post-Christmas/NY ‘Og entry about food! Ian Murray, Ryan Adams and David MacKay posted a small piece on arXiv on Tuesday where they advocate a new type of slice sampler in cases when the posterior distribution on the parameter f is associated with a Gaussian prior,

\pi(f|x) \propto \mathcal{N}(f|0,\Sigma) L(f|x)

and where the update in the Markov chain is based on an elliptic update,

f^\prime = f \cos \theta + \nu \sin\theta,\quad\nu\sim\mathcal{N}(0,\Sigma),

except that \theta is also updated at each MCMC step by a slice sampler. The resulting algorithm is a slice sampler in that it does not reject new values of f^\prime.

I find the proposal interesting, especially because it incorporates a “cyber-parameter” like \theta within the Markov chain, but I wonder how widely the efficiency of the algorithm persists. Indeed, simulating from the prior cannot be very efficient when the likelihood strongly differs from the Gaussian prior. A lack of rejection is not a positive property per se and Gibbs sampling (incl. slice sampling) is notoriously slow for this very lack…

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