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.)

art brut

Italy no-no’s

The Lonely Planet blog has a list of prohibitions on tourists’ activities when visiting some Italian cities. Like Venice, Rome or Milan (below). Most of which is sort of obvious, like not walking around shirtless or barefoot away from beaches, feed the pigeons (although our kids did when visiting Venice for the first time!), hold picnics in busy areas, sit on the Rialto Bridge or the Spanish steps, ride a bike in Venezia!, swim in Trevi Fountain or a Venezia canalo (although kayaking remains allowed outside main canals and working hours), or steal sands from beaches. Some are less predictable, like eating in the street in Florence centre, dress up like an historical (Roman) figure, or wear sandals when hiking. (For the latest one, I got scolded last January when hiking to a waterfall in the Northern tip of Martinique, if not by the police!)

foxhuntshire

French coast