As in previous days, I had an early morn run over the Liberty bridge, with the sunrise as a reward, plus a short swim in the local Sant’ Alviso pool, as I managed to register as a membre this time!, then leading to an hurried breakfast (sad!) not to miss the opening ceremony. My first choice of session was for probabilistic numerics: the first talk was [not Sylvia’s but Lewis Fry’s] Richardson extrapolation by Chris Oates (& coauthors) that causes acceleration in the approximation of functional values (a Taylor expansion at core). Probabilistically numerised via Gaussian processes. Solving linear systems by Jon Cockayne (et al, 2021), with acceleration of iterative methods like conjugate gradient again via Gaussian processing, requiring some knowledge about the condition number of the matrix involved in the linear equations. Interestingly realising the UQ is poor. And Masha Naslidnyk on maximum mean discrepancy likelihood free inference. Since the MMD cannot be computed in closed form, it is approximated via an RKHS kernel and showing that the resulting upper bound converges an optimal rate, achieving thus better precision with less evaluations. MMD has been used in several instances in the ABC literature as well as for generalised Bayesian inference (e.g. by Pierre Alquier or Rito Dutta and their coauthors). Missing other interesting parallel sessions like Data Integration organised by David Rossell.
Also, I chaired the Foundation lecture of my long time friend Kerrie Mengersen on the future of Bayesian analysis, going through many of the projects she drove over the past years (decades!) of modelling via Bayesian statistics in a variety of actual settings, solving challenges of correcting data, reducing dimension, producing complex interfaces with data providers and users. While we had to stop for the following session, it felt like the discussion could have gone on forever! (And a great line of Hakuna my data glimpsed from a passing slide!)
The second multiple session i attended was on Optimal transport and Bayesian learning, with Long Nguyen (who kindly invited to and even more kindly hosted me through Ho Chi Min City last summer) proposing a Wasserstein dendrogram to cluster in mixture models. Which seems to depend much on the parameterisation and the distance, if I understood his presentation. DIC made an appearance but this meant the Dendrogram Information Criterion! Then Hugo Lavenant talked about merging of opinions as how quickly two different priors come to agree when the data size increases. In a non-parametric setting, using a completely random measure framework, with two different measures and optimal transport distances. And then Ricardo Baptista considered intractable posteriors to build sort of a normalising flow (as indicated later). Assuming availability of joint samples from the prior x predictive density and using a triangular transform that favours the marginal x posterior decomposition.
Congrats to our PhD student Emma Kopp who won the best applied presentation at BAYSM on Sunday!!!
