O-Bayes15 [day #1]

vale3So here we are back together to talk about objective Bayes methods, and in the City of Valencià as well.! A move back to a city where the 1998 O’Bayes took place. In contrast with my introductory tutorial, the morning tutorials by Luis Pericchi and Judith Rousseau were investigating fairly technical and advanced, Judith looking at the tools used in the frequentist (Bernstein-von Mises) analysis of priors, with forays in empirical Bayes, giving insights into a wide range of recent papers in the field. And Luis covering works on Bayesian robustness in the sense of resisting to over-influential observations. Following works of him and of Tony O’Hagan and coauthors. Which means characterising tails of prior versus sampling distribution to allow for the posterior reverting to the prior in case of over-influential datapoints. Funny enough, after a great opening by Carmen and Ed remembering Susie, Chris Holmes also covered Bayesian robust analysis. More in the sense of incompletely or mis-  specified models. (On the side, rekindling one comment by Susie and the need to embed robust Bayesian analysis within decision theory.) Which was also much Chris’ point, in line with the recent Watson and Holmes’ paper. Dan Simpson in his usual kick-the-anthill-real-hard-and-set-fire-to-it discussion pointed out the possible discrepancy between objective and robust Bayesian analysis. (With lines like “modern statistics has proven disruptive to objective Bayes”.) Which is not that obvious because the robust approach simply reincorporates the decision theory within the objective framework. (Dan also concluded with the comic strip below, whose message can be interpreted in many ways…! Or not.)

The second talk of the afternoon was given by Veronika Ročková on a novel type of spike-and-slab prior to handle sparse regression, bringing an alternative to the standard Lasso. The prior is a mixture of two Laplace priors whose scales are constrained in connection with the actual number of non-zero coefficients. I had not heard of this approach before (although Veronika and Ed have an earlier paper on a spike-and-slab prior to handle multicolinearity that Veronika presented in Boston last year) and I was quite impressed by the combination of minimax properties and practical determination of the scales. As well as by the performances of this spike-and-slab Lasso. I am looking forward the incoming paper!

The day ended most nicely in the botanical gardens of the University of Valencià, with an outdoor reception surrounded by palm trees and parakeet cries…

3 Responses to “O-Bayes15 [day #1]”

  1. Dan Simpson Says:

    I’m happy to admit that there is a gap between my understanding of the scope of objective bayes before and after this meeting (I went in with the perhaps not uncommon notion that this was mainly reference priors and other model-derived things). So more properly the perceived incompatibility is with a narrow subclass of objective Bayes.

    (Perhaps the next o-Bayes discussion paper in Bayesian Analysis should be about the types of objectives. If for no other reason than someone can then write a comment called “Objections to the objectives of Objective Bayes”)

    I still stand by the disruptive comment, mainly because that’s what makes the field alive.

    • Dan Simpson Says:

      Incidentally, this idea of “objective Bayes” as “priors built from/for objectives” rather than “priors that let the data speak” is really exciting to me!

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