mostly MC[bruary]

insufficient Gibbs at One World ABC [25/01]

The next [on-line] One World Approximate Bayesian Computation (ABC) Seminar will be delivered by Antoine Luciano, currently writing his PhD with Robin Ryder and I. It will take place at 9am, UK/GMT time, on Thursday 25 January, with members of the stats lab here in CEREMADE attending Antoine’s lecture live at the PariSanté campus. Here is the abstract for the talk:

In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns, and only aggregated, robust and inefficient statistics derived from the data are accessible. These robust statistics are not sufficient, but they demonstrate reduced sensitivity to outliers and offer enhanced data protection due to their higher breakdown point. In this article, operating within a parametric framework, we propose a method to sample from the posterior distribution of parameters conditioned on different robust and inefficient statistics: specifically, the pairs (median, MAD) or (median, IQR), or one or more quantiles. Leveraging a Gibbs sampler and the simulation of latent augmented data, our approach facilitates simulation according to the posterior distribution of parameters belonging to specific families of distributions. We demonstrate its applicability on the Gaussian, Cauchy, and translated Weibull families.

based on our recent arXival.

insufficient Gibbs sampling

We have just arXived our paper on insufficient Gibbs sampling with Antoine Luciano and Robin Ryder, from Université Paris Dauphine. This is Antoine’s first paper and part of his PhD. (In particular, he wrote the entire code.) The idea stemmed from a discussion on ABC benchmarks, like the one when the pair (median, MAD) is the only available observation. With no available joint density, the setting seems to prohibit calling for an MCMC sampler. However, simulating the complete data set conditional on these statistics proves feasible, with a bit of bookkeeping. With obviously much better results [demonstrated above for a Cauchy example] than when calling ABC and at a very similar cost. (If not accounting for the ability of ABC to be parallelised.)  The idea can be extended to other settings, obviously, as long as completion remains achievable. (And a big thanks to our friend Ed George who suggested the title, while at CIRM. I had suggested “Gibbs for boars” as a poster title, in connection with the historical time-line of

Gibbs for Kids (Casella and George) — Gibbs for Pigs (Gianola) — Gibbs for Robust Pigs = Gibbs for Boars

and the abundance of boars on the Luminy campus, but this did not sound convincing enough for Antoine.)

Bayesian restricted likelihood with insufficient statistic [slides]

A great Bayesian Analysis webinar this afternoon with well-balanced presentations by Steve MacEachern and John Lewis, and original discussions by Bertrand Clarke and Fabrizio Rugieri. Which attracted 122 participants. I particularly enjoyed Bertrand’s points that likelihoods were more general than models [made in 6 different wordings!] and that this paper was closer to the M-open perspective. I think I eventually got the reason why the approach could be seen as an ABC with ε=0, since the simulated y’s all get the right statistic, but this presentation does not bring a strong argument in favour of the restricted likelihood approach, when considering the methodological and computational effort. The discussion also made me wonder if tools like VAEs could be used towards approximating the distribution of T(y) conditional on the parameter θ. This is also an opportunity to thank my friend Michele Guindani for his hard work as Editor of Bayesian Analysis and in particular for keeping the discussion tradition thriving!

BA webinar with discussion