Barker (from the lovely city of Dunedin) and Link published a paper in the American Statistician last September that I missed, as I missed their earlier email about the paper since it arrived The Day After… The paper is about a new specification of RJMCMC, almost twenty years after Peter Green’s (1995) introduction of the method. The authors use the notion of a palette, “from which all model specific parameters can be calculated” (in a deterministic way). One can see the palette ψ as an intermediary step in the move between two models. This reduces the number of bijections, if not the construction of the dreaded Jacobians!, but forces the construction of pseudo-priors on the unessential parts of ψ for every model. Because the dimension of ψ is fixed, a Gibbs sampling interleaving model index and palette value is then implementable. The conditional of the model index given the palette is available provided there are not too many models under competitions, with the probabilities recyclable towards a Rao-Blackwell approximation of the model probability. I wonder at whether or not another Rao-Blackwellisation is possible, namely to draw from all the simulated palettes a sample for the parameter of an arbitrarily chosen model.
Archive for New Zealand
In what seems to become a X’mas tradition, I went back to see a Hobbit movie with my kids. (If not in a Norman theatre, which permitted us to hear the original soundtrack.) And once more, we came out of the movie theatre with different reactions. Both my son and I thought it was better than the (very boring) first instalment. My daughter did not buy the dragon part (which is indeed difficult to buy!) and complained about the lack of depth and of this feeling of history and tradition that should come with elves. I completely agree with her analysis on this second part. The movie is too centred on action scenes—the park-ridesque escape from the Halls of Thranduil and the pursuit by the orcs, themselves pursued by the elves Legolas and Tauriel are definitely lacking in subtlety!—to spend time on the history of the land, and on the reasons for the behaviour of the elves towards the dwarves, or on the past glory of Dale… The New-Zealand mountain landscapes are as beautiful as ever, but lack in bringing strength to the story, a band of orgs on wargs against a thin ridge in the rising sun replacing a company of dwarves on a moor against a beautiful sunset in the mountains in the previous film. Smaug is also a delicate topic: it is beautifully played by Cumberbatch, who gave more than his voice to the dragon. (And the irony of having Smaug getting the higher ground in his conversation with Bilbo, just like Holmes getting the better of Watson in the BBC series!) Nonetheless, the last third of the film when the dwarves face him is altogether unconvincing, missing the subtle and hypnotic features of dragons and somehow making Smaug appear more like the dragon in Shrek… The trick of the final scene eventually worked out for me, but the preliminaries were so unconvincing. Having Smaug playing hide and seek with the group of dwarves, while destroying the halls of Erebor, is contradicting the reputation for deep cunning (Μῆτις) of the dragons! The last point I want to make is somehow of lesser importance: Peter Jackson chose to move away from the book in many more ways in this second film, when compared with the first one. This is not an issue in that no movie can reproduce the most notable features of the book, so changes would be welcomed had they brought a more epic tone to the Quest. Alas, this is not the case and the scenes of Gandalf in dol Guldur make him sound like an incompetent beginner, while the inclusions of Tauriel and of the corrupted Master of Laketown branch off the main theme with a superfluous love triangle and with an unnecessary depiction of greed, once again taking some precious time off from setting the journey more safely into its epic dimension. Not too mention the additional tension created by the orcish pursuit. All in all, not an unpleasant film, but much lighter than it could have been…
We present a novel method for averaging a sequence of histogram states visited by a Metropolis-Hastings Markov chain whose stationary distribution is the posterior distribution over a dense space of tree-based histograms. The computational efficiency of our posterior mean histogram estimate relies on a statistical data-structure that is sufficient for non-parametric density estimation of massive, multi-dimensional metric data. This data-structure is formalized as statistical regular paving (SRP). A regular paving (RP) is a binary tree obtained by selectively bisecting boxes along their first widest side. SRP augments RP by mutably caching the recursively computable sufficient statistics of the data. The base Markov chain used to propose moves for the Metropolis-Hastings chain is a random walk that data-adaptively prunes and grows the SRP histogram tree. We use a prior distribution based on Catalan numbers and detect convergence heuristically. The L1-consistency of the the initializing strategy over SRP histograms using a data-driven randomized priority queue based on a generalized statistically equivalent blocks principle is proved by bounding the Vapnik-Chervonenkis shatter coefficients of the class of SRP histogram partitions. The performance of our posterior mean SRP histogram is empirically assessed for large sample sizes simulated from several multivariate distributions that belong to the space of SRP histograms.
The paper actually appeared in the special issue of TOMACS Arnaud Doucet and I edited last year. It is coauthored by Dominic Lee, Jennifer Harlow and Gloria Teng. Unfortunately, Raazesh could not connect to our video-projector. Or fortunately as he gave a blackboard talk that turned to be fairly intuitive and interactive.
A few days ago, Dennis Prangle, Paul Fernhead, and their co-authors from New Zealand have posted on arXiv their (long-awaited) study of the selection of summary statistics for ABC model choice. And I read it during my trip to England, in trains and planes, if not when strolling in the beautiful English countryside as above.
As posted several times on this ‘Og, the crux of the analysis is that the Bayes factor is a good type of summary when comparing two models, this result extending to more model by considering instead the vector of evidences. As in the initial Read Paper by Fearnhead and Prangle, there is no true optimality in using the Bayes factor or vector of evidences, strictly speaking, besides the fact that the vector of evidences is minimal sufficient for the marginal models (integrating out the parameters). (This was a point made in my discussion.) The implementation of the principle is similar to this Read Paper setting as well: run a pilot ABC simulation, estimate the vector of evidences, and re-run the main ABC simulation using this estimate as the summary statistic. The paper contains a simulation study using some of our examples (in Marin et al., 2012), as well as an application to genetic bacterial data. Continue reading
On X’mas evening, I went to the movies with both my kids, such a rare event it deserves a special mention! Unsurprisingly, the common denominator for the three of us was The Hobbit (I), on its second week. The small Norman cinema where we went was far from packed, no wonder for a X’mas evening, and it reminded me of the time I took my brother-in-laws to see Time Bandits in the same room, with a crowd close to 12 people total! (Yes, it was a while ago, as Time Bandits came out about 1981…!)
Anyway, we watched the movie together and came out with divided opinions! My daughter liked it, my son thought it was not as good as the Lord of the Rings, not enough fighting maybe?, or simply less convincing orcs, and above all a missing Legolas!, and I considered the whole affair just ridiculous! I had misgivings from the start as Tolkien’s Hobbit is a kids book, which does not make for a proper setting for Jackson’s usually grandiose fantasy operas… It is also a short book and I could not see why it required three movies altogether! Well, I still do not see, except for providing the producers with more revenues. Continue reading