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.)

la belle sauvage [book review]

Another book I brought back from Austin. And another deeply enjoyable one, although not the end of a trilogy of trilogies this time. This book, La Belle Sauvage, is first in a new trilogy by Philip Pullman that goes back to the early infancy of the hero of His Dark Materials, Lyra. Later volumes will take place after the first trilogy.

This is very much a novel about Oxford, to the point it sometimes seems written only for people with an Oxonian connection. After all, the author is living in Oxford… (Having the boat of the two characters passing by the [unnamed] department of Statistics at St. Giles carried away by the flood was a special sentence for me!)

Also, in continuation of His Dark Materials, a great steampunk universe, with a very oppressive Church and so far a limited used of magicks! Limited to the daemons, again in continuation with past volumes…

Now, some passages of the book remind me of Ishiguro’s buried giant, in the sense that the characters meeting myths from other stories may “really” meet them or instead dream. This is for instance the case when they accost at a property where an outworldy party is taking place and no-one is noticing them. Or when they meet a true giant that is a river deity, albeit not in the spirit of Ben Aaronovitch’s Rivers of London novels.

The story is written in the time honoured setup of teenager discovery travels, with not so much to discover as the whole country is covered by water. And the travel gets a wee bit boring after a while, with a wee bit too many coincidences, the inexplicable death (?) of a villain, and an hurried finale, where the reverse trip of the main characters takes a page rather than one book…

Trivia: La Belle Sauvage was also the name of the pub in Ludgate Hill where Pocahontas and her brother Tomocomo stayed when they first arrived in London. And The Trout is a true local pub, on the other side of Port Meadow [although I never managed to run that far in that direction while staying in St. Hugh, Oxford, last time, the meadow being flooded!].

Looking forward the second volume (already written, so no risk of The Name of the Wind or Game of Thrones quagmires, i.e., an endless wait for the next volume!), hoping the author keeps up the good work, the right tension in the story, and avoids by all means parallel universes, which were so annoying in the first trilogy! (I do remember loosing interest in the story during the second book and having trouble finishing the third one. I am not sure my son [who started before me] ever completed the trilogy…)

The Hanging Tree

This is the fifth sixth volume of Ben Aaronovitch’s Rivers of London series. Which features PC Peter Grant from the London’s Metropolitan Police specialising in paranormal crime. Joining a line of magicians that was started by Isaac Newton. And with the help of water deities. Although this English magic sleuthing series does not compare with the superlative Jonathan Strange & Mr. Norrell single book, The Hanging Tree remains highly enjoyable, maybe more for its style and vocabulary than for the detective story itself, which does not sound completely coherent (unless I read it too quickly during the wee hours in Banff last week). And does not bring much about this part of London. Still a pleasure to read as the long term pattern of Aaronovitch’s universe slowly unravels and some characters get more substance and depth.

broken homes [book review]

Even though this is the fourth volume in the Peter Grant series, I did read it first [due to my leaving volume one in my office in Coventry and coming across this one in an airport bookstore in Düsseldorf], an experiment I do not advise anyone to repeat as it kills some of the magic in Rivers of London [renamed Midnight Riots on the US market, for an incomprehensible reason!, with the series being recalled Rivers of London, but at least they left the genuine and perfect covers…, not like some of the other foreign editions!] and makes reading Broken homes an exercise in guessing. [Note for ‘Og’s readers suffering from Peter Grant fatigue: the next instalment, taking the seemingly compulsory trip Outside!—witness the Bartholomew series—, is waiting for me in Warwick, so I will not read it before the end of January!]

“I nodded sagely. `You’re right,’ I said. `We need a control.’
`Seriously?’she asked.
`Otherwise, how do you know the variable you’ve changed is the one having the effect?’ I said.”

Now, despite this inauspicious entry, I did enjoy Broken homes as much [almost!] as the other volumes in the series. It mostly takes place in a less familiar [for a French tourist like me] part of London, but remains nonetheless true to its spirit of depicting London as a living organism! There are mostly characters from the earlier novels, but the core of the story is an infamous housing estate built by a mad architect in Elephant and Castle, not that far from Waterloo [Station], but sounding almost like a suburb from Aaronovitch’s depiction! Actually, the author has added a google map for the novel locations on his blog, wish I had it at the time [kind of difficult to get in a plane!].

“Search as I might, nobody else was offering free [wifi] connections to the good people of Elephant and Castle.”

The plot itself is centred on this estate [not really a spoiler, is it?] and the end is outstanding in that it is nothing like one would expect. With or without reading the other volumes. I still had trouble understanding the grand scheme of the main villain, while I have now entirely forgotten about the reasons for the crime scene at the very beginning of Broken homes. Rereading the pages where the driver, Robert Weil, appears did not help. What was his part in the story?! Despite this [maybe entirely personal] gap, the story holds well together, somewhat cemented by the characters populating the estate, who are endowed with enough depth to make them truly part of the story, even when they last only a few pages [spoiler!]. And as usual style and grammar and humour are at their best!

Whispers underground [book review]

“Dr. Walid said that normal human variations were wide enough that you’d need samples of hundreds of subjects to test that. Thousands if you wanted a statistically significant answer.
Low sample size—one of the reasons why magic and science are hard to reconcile.”

This is the third volume in the Rivers of London series, brought back from Gainesville, and possibly the least successful (in my opinion). It indeed takes place underground and not only in the Underground and the underground sewers of London. Which is this literary trick that always irks me in fantasy novels, namely the sudden appearance of massive underground complex with unsuspected societies that are large and evolved enough to reach the Industrial Age. (Sorry if this is too much of a spoiler!)

“It was the various probability calculations that stuffed me—they always do. I’d have been a bad scientist.”

Not that everything is bad in this novel: I still like the massive infodump about London, the style and humour, the return of PC Lesley trying to get over the (literal) loss of her face, and the appearance of new characters. But the story itself, revolving about a murder investigation, is rather shallow and the (compulsory?) English policeman versus American cop competition is too contrived to be funny. Most of the major plot is hidden from this volume, unless there are clues I missed. (For instance, one death from a previous volume which seemed to get ignored at that time is finally explained here.) Definitely not the book to read on its own, as it still relates and borrow much from the previous volumes, but presumably one to read nonetheless as the next instalment, Broken homes.