O’Bayes 19/1 [snapshots]

Although the tutorials of O’Bayes 2019 of yesterday were poorly attended, albeit them being great entries into objective Bayesian model choice, recent advances in MCMC methodology, and the multiple layers of BART, for which I have to blame myself for sticking the beginning of O’Bayes too closely to the end of BNP as only the most dedicated could achieve the commuting from Oxford to Coventry to reach Warwick in time, the first day of talks were well attended, despite weekend commitments, conference fatigue, and perfect summer weather! Here are some snapshots from my bench (and apologies for not covering better the more theoretical talks I had trouble to follow, due to an early and intense morning swimming lesson! Like Steve Walker’s utility based derivation of priors that generalise maximum entropy priors. But being entirely independent from the model does not sound to me like such a desirable feature… And Natalia Bochkina’s Bernstein-von Mises theorem for a location scale semi-parametric model, including a clever construct of a mixture of two Dirichlet priors to achieve proper convergence.)

Jim Berger started the day with a talk on imprecise probabilities, involving the society for imprecise probability, which I discovered while reading Keynes’ book, with a neat resolution of the Jeffreys-Lindley paradox, when re-expressing the null as an imprecise null, with the posterior of the null no longer converging to one, with a limit depending on the prior modelling, if involving a prior on the bias as well, with Chris discussing the talk and mentioning a recent work with Edwin Fong on reinterpreting marginal likelihood as exhaustive X validation, summing over all possible subsets of the data [using log marginal predictive].Håvard Rue did a follow-up talk from his Valencià O’Bayes 2015 talk on PC-priors. With a pretty hilarious introduction on his difficulties with constructing priors and counseling students about their Bayesian modelling. With a list of principles and desiderata to define a reference prior. However, I somewhat disagree with his argument that the Kullback-Leibler distance from the simpler (base) model cannot be scaled, as it is essentially a log-likelihood. And it feels like multivariate parameters need some sort of separability to define distance(s) to the base model since the distance somewhat summarises the whole departure from the simpler model. (Håvard also joined my achievement of putting an ostrich in a slide!) In his discussion, Robin Ryder made a very pragmatic recap on the difficulties with constructing priors. And pointing out a natural link with ABC (which brings us back to Don Rubin’s motivation for introducing the algorithm as a formal thought experiment).

Sara Wade gave the final talk on the day about her work on Bayesian cluster analysis. Which discussion in Bayesian Analysis I alas missed. Cluster estimation, as mentioned frequently on this blog, is a rather frustrating challenge despite the simple formulation of the problem. (And I will not mention Larry’s tequila analogy!) The current approach is based on loss functions directly addressing the clustering aspect, integrating out the parameters. Which produces the interesting notion of neighbourhoods of partitions and hence credible balls in the space of partitions. It still remains unclear to me that cluster estimation is at all achievable, since the partition space explodes with the sample size and hence makes the most probable cluster more and more unlikely in that space. Somewhat paradoxically, the paper concludes that estimating the cluster produces a more reliable estimator on the number of clusters than looking at the marginal distribution on this number. In her discussion, Clara Grazian also pointed the ambivalent use of clustering, where the intended meaning somehow diverges from the meaning induced by the mixture model.

O’Bayes 2019 conference program

The full and definitive program of the O’Bayes 2019 conference in Warwick is now on line. Including discussants for all papers. And the three [and free] tutorials on Friday afternoon, 28 June, on model selection (M. Barbieri), MCMC recent advances (G.O. Roberts) and BART (E.I. George). Registration remains open at the reduced rate and submissions of posters can still be sent to me for all conference participants.

non-identifiability in Venezia

Last Wednesday, I attended a seminar by T. Kitagawa at the economics seminar of the University Ca’ Foscari, in Venice, which was about (uncertain) identifiability and a sort of meta-Bayesian approach to the problem. Just to give an intuition about the setting, a toy example is a simultaneous equation model Ax=ξ, where x and ξ are two-dimensional vectors, ξ being a standard bivariate Normal noise. In that case, A is not completely identifiable. The argument in the talk (and the paper) is that the common Bayesian answer that sets a prior on the non-identifiable part (which is an orthogonal matrix in the current setting) is debatable as it impacts inference on the non-identifiable parts, even in the long run. Which seems fine from my viewpoint. The authors propose to instead consider the range of possible priors that are compatible with the set restrictions on the non-identifiable parts and to introduce a mixture between a regular prior on the whole parameter A and this collection of priors, which can be seen as a set-valued prior although this does not fit within the Bayesian framework in my opinion. Once this mixture is constructed, a formal posterior weight on the regular prior can be derived. As well as a range of posterior values for all quantities of interest. While this approach connects with imprecise probabilities à la Walley (?) and links with robust Bayesian studies of the 1980’s, I always have difficulties with the global setting of such models, which do not come under criticism while being inadequate. (Of course, there are many more things I do not understand in econometrics!)