Archive for Casa Matemática Oaxaca

focused Bayesian prediction

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on June 3, 2020 by xi'an

In this fourth session of our One World ABC Seminar, my friend and coauthor Gael Martin, gave an after-dinner talk on focused Bayesian prediction, more in the spirit of Bissiri et al. than following a traditional ABC approach.  because along with Ruben Loaiza-Maya and [my friend and coauthor] David Frazier, they consider the possibility of a (mild?) misspecification of the model. Using thus scoring rules à la Gneiting and Raftery. Gael had in fact presented an earlier version at our workshop in Oaxaca, in November 2018. As in other solutions of that kind, difficulty in weighting the score into a distribution. Although asymptotic irrelevance, direct impact on the current predictions, at least for the early dates in the time series… Further calibration of the set of interest A. Or the focus of the prediction. As a side note the talk perfectly fits the One World likelihood-free seminar as it does not use the likelihood function!

“The very premise of this paper is that, in reality, any choice of predictive class is such that the truth is not contained therein, at which point there is no reason to presume that the expectation of any particular scoring rule will be maximized at the truth or, indeed, maximized by the same predictive distribution that maximizes a different (expected) score.”

This approach requires the proxy class to be close enough to the true data generating model. Or in the word of the authors to be plausible predictive models. And to produce the true distribution via the score as it is proper. Or the closest to the true model in the misspecified family. I thus wonder at a possible extension with a non-parametric version, the prior being thus on functionals rather than parameters, if I understand properly the meaning of Π(Pθ). (Could the score function be misspecified itself?!) Since the score is replaced with its empirical version, the implementation is  resorting to off-the-shelf MCMC. (I wonder for a few seconds if the approach could be seen as a pseudo-marginal MCMC but the estimation is always based on the same observed sample, hence does not directly fit the pseudo-marginal MCMC framework.)

[Notice: Next talk in the series is tomorrow, 11:30am GMT+1.]

a la casa matemática de Oaxaca [reminiscence]

Posted in Mountains, Running, Travel, University life with tags , , , , , , , , , , on December 2, 2018 by xi'an

As this was my very first trip to the CMO part of CMO-BIRS, as opposed to many visits to BIRS, Banff, here are my impressions about this other mathematical haven, aka resort, aka retreat… First definitely a very loooong trip from Paris (especially when sitting next to three drunk women speaking loudly the whole trip, thankfully incomprehensibly in Russian!), with few connections between Mexico City [airport] and Oaxaca,  adding [for me] a five and a half hour stay over in the airport, where I experimented for the first time a coffin-like “sleep pod” hostel and some welcome rest. But presumably an easier access compared with Calgary for mathematicians from the South and East of the USA. And obviously for those Central and from South Americas.Then, contrary to Banff, the place for the Casa Matemàtica Oaxaca is for the time being essentially a permanently booked hotel, rather than a dedicated conference centre. Facilities are thus less attuned to visiting mathematicians, like missing real desks in bedrooms or working rooms. Still a nice with a very peaceful inner yard (and too small a pool to consider swimming). Actually facilitating interactions when compared with Banff: blackboards in the patios, tables outside, general quiet atmosphere (except for the endlessly barking dogs in the neighbourhood). Of course the huge difference in the weathers between both places does matter. Paradoxically (given the size of Oaxaca City), CMO is more isolated than BIRS, where downtown is a mere five minute walks, even in the middle of winter. Except for the occasional blizzard. But Oaxaca offers a fabulous food scene worth the longer trip!As for outdoors, there is also a swimming pool (Cina). And back streets to run on, even though the presence of stray dogs in about every road making running broken and haphazard (never run by a dog!, which is my rule since a tiny but angry dog bit my ankle in Caracas!). Running splits up hill a few times every morning was great training! There is furthermore the possibility of sport climbing in nearby San Sebastian de Tutla, as I experienced with Aventours, a local guiding company. And bouldering in an even closer gym.

computational statistics and molecular simulation [18w5023]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on November 19, 2018 by xi'an

The last day of the X fertilisation workshop at the casa matematicà Oaxaca, there were only three talks and only half of the participants. I lost the subtleties of the first talk by Andrea Agazzi on large deviations for chemical reactions, due to an emergency at work (Warwick). The second talk by Igor Barahona was somewhat disconnected from the rest of the conference, working on document textual analysis by way of algebraic data analysis (analyse des données) methods à la Benzécri. (Who was my office neighbour at Jussieu in the early 1990s.) In the last and final talk, Eric Vanden-Eijden made a link between importance sampling and PDMP, as an integral can be expressed via a trajectory of a path. A generalisation of path sampling, for almost any ODE. But also a competitor to nested sampling, waiting for the path to reach an Hamiltonian level, without some of the difficulties plaguing nested sampling like resampling. And involving continuous time processes. (Is there a continuous time version of ABC as well?!) Returning unbiased estimators of mean (the original integral) and variance. Example of a mixture example in dimension d=10 with k=50 components using only 100 paths.

computational statistics and molecular simulation [18w5023]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on November 16, 2018 by xi'an

This Thursday, our X fertilisation workshop at the interface between molecular dynamics and Monte Carlo statistical methods saw a wee bit of reduction in the audience as some participants had already left Oaxaca. Meaning they missed the talk of Christophe Andrieu on hypocoercivity which could have been another hand-on lecture, given the highly pedagogical contents of the talk. I had seen some parts of the talk in MCqMC 2018 in Rennes and at NUS, but still enjoyed the whole of it very much, and so did the audience given the induced discussion. For instance, previously, I had not seen the connection between the guided random walks of Gustafson and Diaconis, and continuous time processes like PDMP. Which Christophe also covered in his talk. (Also making me realise my colleague Jean Dolbeault in Dauphine was strongly involved in the theoretical analysis of PDMPs!) Then Samuel Power gave another perspective on PDMPs. With another augmentation, connected with time, what he calls trajectorial reversibility. This has the impact of diminishing the event rate, but creates some kind of reversibility which seems to go against the motivation for PDMPs. (Remember that all talks are available as videos on the BIRS webpage.) A remark in the talk worth reiterating is the importance of figuring out which kinds of approximations are acceptable in these approximations. Connecting somewhat with the next talk by Luc Rey-Bellet on a theory of robust approximations. In the sense of Poincaré, Gibbs, Bernstein, &tc. concentration inequalities and large deviations. With applications to rare events.The fourth and final “hand-on” session was run by Miranda Holmes-Certon on simulating under constraints. Motivated by research on colloids. For which the overdamp Langevin diffusion applies as an accurate model, surprisingly. Which makes a major change from the other talks [most of the workshop!] relying on this diffusion. (With an interesting intermede on molecular velcro made of DNA strands.) Connected with this example, exotic energy landscapes are better described by hard constraints. (Potentially interesting extension to the case when there are too many constraints to explore all of them?) Now, the definition of the measure projected on the manifold defined by the constraints is obviously an important step in simulating the distribution, which density is induced by the gradient of the constraints ∇q(x). The proposed algorithm is in the same spirit as the one presented by Tony the previous day, namely moving along the tangent space then on the normal space to get back to the manifold. A solution that causes issues when the gradient is (near) zero. A great hand-on session which induced massive feedback from the audience.

In the afternoon session, Gersende Fort gave a talk on a generalisation of the Wang-Landau algorithm, which modifies the true weights of the elements of a partition of the sampling space, to increase visits to low [probability] elements and jumps between modes. The idea is to rely on tempered versions of the original weights, learned by stochastic approximation. With an extra layer of adaptivity. Leading to an improvement with parameters that depends on the phase of the stochastic approximation. The second talk was by David Sanders on a recent paper in Chaos about importance sampling for rare events of (deterministic) billiard dynamics. With diffusive limits which tails are hard to evaluate, except by importance sampling. And the last talk of the day was by Anton Martinsson on simulated tempering for a molecular alignment problem. With weights of different temperatures proportional to the inverse of the corresponding normalising constants, which themselves can be learned by a form of bridge sampling  if I got it right.

On a very minor note, I heard at breakfast a pretty good story from a fellow participant having to give a talk at a conference that was moved to a very early time in the morning due to an official appearing at a later time and as a result “enjoying” a very small audience to the point that a cleaning lady appeared and started cleaning the board as she could not conceive the talks had already started! Reminding me of this picture at IHP.

Oaxaca sunrise [#2]

Posted in Mountains, pictures, Running with tags , , , , , , , on November 15, 2018 by xi'an