reciprocal importance sampling

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.)

Chez Guy**(*)

While I rarely enter company sweepstakes and lotteries (and correlatively never win!), I answered a contest from my credit card company around the 2022 Beijing Winter Olympics, and won the prize of having a Chinese dinner cooked at home by a chef, news that I first treated as a spam for being so improbable. The communication agency in charge of the rewards insisted enough and offered the alternative choice of a top restaurant, which we eventually opted as Guy Savoy in Paris. We went there for lunch last week and enjoyed tremendously the unique experience!, from the location in the historical French Mint, with a monumental entrance, and tables overlooking the Seine,

 

to the round of dishes, colour themes and fabulous tastes, the apex being the hardly coked lobster!,
 

to chatting with the sommelier about unknown vintages and the staff about the dishes, and of course having a great time altogether!
 

 

Kimono exhibition

Taking advantage of the 01 May break and a relatively low density of people in Paris, we went to the Musée du Quai Branly to see a soon to close exhibit on kimonos, with many pieces loaned from Japanese collections, through an exhibit designed by the Victoria and Albert Museum in London. The collection is amazing, especially the most historical part, and illustrates the complex social codes behind this seemingly simple garnment, from a huge variety of materials and techniques, to the Edo era restrictions on whom could wear which type and which printing. And the subtle subversions from the merchant class (and actors, as for this 19th “I do not care” kimono that reminded me of a much more recent outcry!). Highly enjoyable (if slightly crowded!).

Napaljarri-wanu Jukurrpa

jeune fille à la perle [street art]