Archive for Angkor Wat

Guiana impressions [#1]

Posted in Books, Kids, Mountains, pictures, Running, Travel with tags , , , , , , , , , , , , , , , , , , , , , , , , on January 16, 2022 by xi'an

As our daughter Rachel has started her (five year) medical residency with a semester round in a French Guiana hospital, we took the opportunity of the Xmas break and of acceptable travel restrictions to visit her and the largest (and sole American) French departement for a week! This was a most unexpected trip that we enjoyed considerably.

While hot and humid is not my favourite type of weather (!) the weather remained quite tolerable that week, esp. when considering this was the start of the rain season (guiana means land of plentiful water in Arawak!) This made hiking on the (well-traced) paths in the local equatorial rain forest rather interesting, as the red soil is definitely muddy or worse. I however faced much less insects than I feared and mosquito bites were rare beyond the dawn and dusk periods. Plenty of birds, albeit mostly invisible. Except for the fantastic marshes of Kaw, where the variety of birds is amazing, including aras and toucans. Very muddy trails, did I mention it, but beautiful explosion of trees. Green everywhere.My first sight of a sloth was quite the treat, but I regret not spotting anteaters. Or a tapir. Swimming in the marshes of Kaw was great as well, with no worry from local caimans! Which we went spotting after nightfall. The place reminded me in several ways of Tonlé Sap lake, near Angkor.

Ate there an atipa bosco fish from the same place. Which has samurai armor. And two front legs to move outside water! As we had no say in what was served, we also ate paca meat in this restaurant, the agouti paca being a local rodent. Unfortunately because bush meat should not be served to tourists for fear of reducing the animal populations.

Visited several remains of former penal colonies, the whole country being a French penal colony at a not-so-distant-time, from the era when Louisiana was sold to the U.S. to the abolition in 1938, only implemented in 1953… Appalling to think that political and criminal prisoners were sent there to slowly rot to death, with no economical purpose on top of it! To the point of dead prisoners being immersed at sea rather than buried on island gallows, the local cemetery being reserved to guardians and their families….

optimal choice among MCMC kernels

Posted in Statistics with tags , , , , , , , , , , on March 14, 2019 by xi'an

Last week in Siem Reap, Florian Maire [who I discovered originates from a Norman town less than 10km from my hometown!] presented an arXived joint work with Pierre Vandekerkhove at the Data Science & Finance conference in Cambodia that considers the following problem: Given a large collection of MCMC kernels, how to pick the best one and how to define what best means. Going by mixtures is a default exploration of the collection, as shown in (Tierney) 1994 for instance since this improves on both kernels (esp. when each kernel is not irreducible on its own!). This paper considers a move to local weights in the mixture, weights that are not estimated from earlier simulations, contrary to what I first understood.

As made clearer in the paper the focus is on filamentary distributions that are concentrated nearby lower-dimension sets or manifolds Since then the components of the kernel collections can be restricted to directions of these manifolds… Including an interesting case of a 2-D highly peaked target where converging means mostly simulating in x¹ and covering the target means mostly simulating in x². Exhibiting a schizophrenic tension between the two goals. Weight locally dependent means correction by Metropolis step, with cost O(n). What of Rao-Blackwellisation of these mixture weights, from weight x transition to full mixture, as in our PMC paper? Unclear to me as well [during the talk] is the use in the mixture of basic Metropolis kernels, which are not absolutely continuous, because of the Dirac mass component. But this is clarified by Section 5 in the paper. A surprising result from the paper (Corollary 1) is that the use of local weights ω(i,x) that depend on the current value of the chain does jeopardize the stationary measure π(.) of the mixture chain. Which may be due to the fact that all components of the mixture are already π-invariant. Or that the index of the kernel constitutes an auxiliary (if ancillary)  variate. (Algorithm 1 in the paper reminds me of delayed acceptance. Making me wonder if computing time should be accounted for.) A final question I briefly discussed with Florian is the extension to weights that are automatically constructed from the simulations and the target.

asymptotics of synthetic likelihood

Posted in pictures, Statistics, Travel with tags , , , , , , , , , , on March 11, 2019 by xi'an

David Nott, Chris Drovandi and Robert Kohn just arXived a paper on a comparison between ABC and synthetic likelihood, which is both interesting and timely given that synthetic likelihood seems to be lacking behind in terms of theoretical evaluation. I am however as puzzled by the results therein as I was by the earlier paper by Price et al. on the same topic. Maybe due to the Cambodia jetlag, which is where and when I read the paper.

My puzzlement, thus, comes from the difficulty in comparing both approaches on a strictly common ground. The paper first establishes convergence and asymptotic normality for synthetic likelihood, based on the 2003 MCMC paper of Chernozukov and Hong [which I never studied in details but that appears like the MCMC reference in the econometrics literature]. The results are similar to recent ABC convergence results, unsurprisingly when assuming a CLT on the summary statistic vector. One additional dimension of the paper is to consider convergence for a misspecified covariance matrix in the synthetic likelihood [and it will come back with a revenge]. And asymptotic normality of the synthetic score function. Which is obviously unavailable in intractable models.

The first point I have difficulty with is how the computing time required for approximating mean and variance in the synthetic likelihood, by Monte Carlo means, is not accounted for in the comparison between ABC and synthetic likelihood versions. Remember that ABC only requires one (or at most two) pseudo-samples per parameter simulation. The latter requires M, which is later constrained to increase to infinity with the sample size. Simulations that are usually the costliest in the algorithms. If ABC were to use M simulated samples as well, since it already relies on a kernel, it could as well construct [at least on principle] a similar estimator of the [summary statistic] density. Or else produce M times more pairs (parameter x pseudo-sample). The authors pointed out (once this post out) that they do account for the factor M when computing the effective sample size (before Lemma 4, page 12), but I still miss why the ESS converging to N=MN/M when M goes to infinity is such a positive feature.

Another point deals with the use of multiple approximate posteriors in the comparison. Since the approximations differ, it is unclear that convergence to a given approximation is all that should matter, if the approximation is less efficient [when compared with the original and out-of-reach posterior distribution]. Especially for a finite sample size n. This chasm in the targets becomes more evident when the authors discuss the use of a constrained synthetic likelihood covariance matrix towards requiring less pseudo-samples, i.e. lower values of M, because of a smaller number of parameters to estimate. This should be balanced against the loss in concentration of the synthetic approximation, as exemplified by the realistic examples in the paper. (It is also hard to see why M could be not of order √n for Monte Carlo reasons.)

The last section in the paper is revolving around diverse issues for misspecified models, from wrong covariance matrix to wrong generating model. As we just submitted a paper on ABC for misspecified models, I will not engage into a debate on this point but find the proposed strategy that goes through an approximation of the log-likelihood surface by a Gaussian process and a derivation of the covariance matrix of the score function apparently greedy in both calibration and computing. And not so clearly validated when the generating model is misspecified.

Angkor finale [jatp]

Posted in pictures, Travel with tags , , , , , , , , on March 7, 2019 by xi'an

Angkor roots [jatp]

Posted in Statistics with tags , , , , , on March 5, 2019 by xi'an

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