Foundations of objective Bayesian methodology [21w5107]

After years in the making (!), our BIRS-CMO workshop on the foundations of O’Bayes is at last taking place! In an hybrid format as BIRS-CMO is restricting the attendance to 15 people on site, instead of the customary (i.e., pre-COVID) 35. Still, it is quite exciting to join this workshop and the friends who will gather in Mexico or on-line to discuss objective Bayesian tools and prospects. And of course to visit for the second time the city of Oaxaca, its temples and markets! (Hopefully managing the stray dogs when running. If running.)

end-to-end Bayesian learning [CIRM]

Next Fall, there will be a workshop at CIRM, Luminy, Marseilles, on Bayesian learning. It takes place 22-29 October 2021 on this wonderful campus at the border with the beautiful Parc National des Calanques, in a wonderfully renovated CIRM building and involves friends and colleagues of mine as organisers and plenary speakers. (I am not involved!, but plan to organise a scalable MCMC workshop there the year after!) The conference is well-supported and the housing fees will be minimal since the centre is also subsidized by CNRS. The deadline for contributed talks and posters is 22 March, while it is 15 June for registration. Hopefully by this time the horizon will have cleared up enough to consider traveling and meeting again. Hopefully. (In which case I will miss this wonderful conference due to other meeting and teaching commitments in the Fall.)

non-reversible gerrymandering

Gregory Herschlag, Jonathan C. Mattingly [whom I met in Oaxaca and who acknowledges helpful conversations with Manon Michel while at CIRM two years ago], Matthias Sachs, and Evan Wyse just posted an arXiv paper using non-reversible MCMC methods to improve sampling of voting district plans towards fighting (partisan) Gerrymandering. In doing so we extend thecurrent framework for construction of non-reversible Markov chains on discrete samplingspaces by considering a generalization of skew detailed balance. Since this means sampling in a discrete space, the method using lifting. Meaning adding a dichotomous dummy variable, “based on a notion of flowing the center of mass of districts along a defined vector field”. The paper is quite detailed about the validation and the implementation of the method. With this interesting illustration for the mixing properties of the different versions:

 

post-COVID post-conference mood

Nature ran a 4-page comment on the post-COVID future of massive conferences (NeurIPS or JSM style) and on how to make them less carbon greedy. Some of their common-sense suggestions come close to what I had suggested a while ago and some became promptly implemented in these times of COVID-19 travel restrictions, as, e.g., to systematically include virtual attendance option(s), with provisions from one’s institutions for quality time (as if one was indeed away), to add multiple (3?) regional hubs to a single location, which also offers the perk of a round-the-clock meeting, with an optimisation of the three places chosen to minimise (estimated) total flight distances for the potential participants, as in e.g. choosing U.S. central Chicago rather than extremes like Seattle or Miami, and possibly adding Tokyo and Paris, to reduce the frequency of the monster meetings by coordinating with sister societies, to enforce an individual or institutional maximum yearly budget, to have corporate sponsors turning from travel support to improving remote access in less favoured countries.

Obviously, it seems difficult to completely switch to a fully virtual solution, as attending a conference has many academic dimensions to be accounted for, but the “big ones” should be the first to shrink, if only because the most impacting. And also because small, high quality workshops have much more impact research-wise on their attendants. With the above still offering some savings. And also the possibility to bypass financial, personal, visa, political, life-threatening impossibilities to attend a meeting in a specific foreign country. Provided uncensored remote communication tools are allowed or possible from the said  country. (Calling for the question, barring financial difficulties, and once COVID-related restrictions have been lifted, what are the countries where everyone could consider attending?!)

This year, before lockdown forced the cancellation of ABC in Grenoble, we had set a mirror version in Warwick. Which led us to create the One World ABC seminar. The Bernoulli-IMS World congress was postponed by one year but a few dedicated volunteers managed to build within a few weeks a free impressive virtual substitute with more than 600 talks and close to 2000 participants (so far). Remember it is to take place on 24-28 August, on different time zones and with ten live plenaries repeated twice to this effect.

Next year, we still hope to organise an Objective Bayesian workshop at Casa Matemática Oaxaca (CMO) in México and the current sanitary conditions imply a reduction of the physically present participants by two thirds. Meaning for certain a remote component and possibly a mirror location depending on the state of the World in December 2021.

focused Bayesian prediction

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(P_θ). (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.]