The next O’Bayes meeting (more precisely the International Workshop on Objective Bayes Methodology, O-Bayes15), will take place in València, Spain, on June 1-4, 2015. This is the second time an O’Bayes conference takes place in València, after the one José Miguel Bernardo organised in 1998 there. The principal objectives of O-Bayes15 will be to facilitate the exchange of recent research developments in objective Bayes theory, methodology and applications, and related topics (like limited information Bayesian statistics), to provide opportunities for new researchers, and to establish new collaborations and partnerships. Most importantly, O-Bayes15 will be dedicated to our friend Susie Bayarri, to celebrate her life and contributions to Bayesian Statistics. Check the webpage of O-Bayes15 for the program (under construction) and the practical details. Looking forward to the meeting and hopeful for a broadening of the basis of the O’Bayes community and of its scope!
Archive for objective Bayes
Today I gave a talk in the Advances in model selection session. Organised by Veronika Rockova and Ed George. (A bit of pre-talk stress: I actually attempted to change my slides at 5am and only managed to erase the current version! I thus left early enough to stop by the presentation room…) Here are the final slides, which have much in common with earlier versions, but also borrowed from Jean-Michel Marin’s talk in Cambridge. A posteriori, I think the talk missed one slide on the practical run of the ABC random forest algorithm, since later questions showed miscomprehension from the audience.
The other talks in this session were by Andreas Buja [whom I last met in Budapest last year] on valid post-modelling inference. A very relevant reflection on the fundamental bias in statistical modelling. Then by Nick Polson, about efficient ways to compute MAP for objective functions that are irregular. Great entry into optimisation methods I had never heard of earlier.! (The abstract is unrelated.) And last but not least by Veronika Rockova, on mixing Indian buffet processes with spike-and-slab priors for factor analysis with unknown numbers of factors. A definitely advanced contribution to factor analysis, with a very nice idea of introducing a non-identifiable rotation to align on orthogonal designs. (Here too the abstract is unrelated, a side effect of the ASA requiring abstracts sent very long in advance.)
Although discussions lasted well into the following Bayesian Inference: Theory and Foundations session, I managed to listen to a few talks there. In particular, a talk by Keli Liu on constructing non-informative priors. A question of direct relevance. The notion of objectivity is to achieve a frequentist distribution of the Bayes factor associated with the point null that is constant. Or has a constant quantile at a given level. The second talk by Alexandra Bolotskikh related to older interests of mine’s, namely the construction of improved confidence regions in the spirit of Stein. (Not that surprising, given that a coauthor is Marty Wells, who worked with George and I on the topic.) A third talk by Abhishek Pal Majumder (jointly with Jan Hanning) dealt on a new type of fiducial distributions, with matching prior properties. This sentence popped a lot over the past days, but this is yet another area where I remain puzzled by the very notion. I mean the notion of fiducial distribution. Esp. in this case where the matching prior gets even closer to being plain Bayesian.
This was the first day of our workshop Advances in Scalable Bayesian Computation and it sounded like the “main” theme was probabilistic programming, in tune with my book review posted this morning. Indeed, both Vikash Mansinghka and Frank Wood gave talks about this concept, Vikash detailing the specifics of a new programming language called Venture and Frank focussing on his state-space version of the above called Anglican. This is a version of the language Church, developed to handle probabilistic models and inference (hence the joke about Anglican, “a Church of England Venture’! But they could have also added that Frank Wood was also the name of a former archbishop of Melbourne..!) I alas had an involuntary doze during Vikash’s talk, which made it harder for me to assess the fundamentals of those ventures, of how they extended beyond a “mere” new software (and of why I would invest in learning a Lisp-based language!).
The other talks of Day #1 were of a more “classical” nature with Pierre Jacob explaining why non-negative unbiased estimators were impossible to provide in general, a paper I posted about a little while ago, and including an objective Bayes example that I found quite interesting. Then Sumeet Singh (no video) presented a joint work with Nicolas Chopin on the uniform ergodicity of the particle Gibbs sampler, a paper that I should have commented here (except that it appeared just prior to The Accident!), with a nice coupling proof. And Maria Lomeli gave us an introduction to the highly general Poisson-Kingman mixture models as random measures, which encompasses all of the previously studied non-parametric random measures, with an MCMC implementation that included a latent variable representation for the alpha-stable process behind the scene, representation that could be (and maybe is) also useful in parametric analyses of alpha-stable processes.
We also had an open discussion in the afternoon that ended up being quite exciting, with a few of us voicing out some problems or questions about existing methods and others making suggestions or contradictions. We are still a wee bit short of considering a collective paper on MCMC under constraints with coherent cross-validated variational Bayes and loss-based pseudo priors, with applications to basketball data” to appear by the end of the week!
Add to this two visits to the Sally Borden Recreation Centre for morning swimming and evening climbing, and it is no wonder I woke up a bit late this morning! Looking forward Day #2!
Here are the slides of my tutorial at O’ Bayes 2013 today, a pot-pourri of various, recent and less recent, criticisms (with, albeit less than usual, a certain proportion of recycled slides):
On my way to Duke and O’Bayes 2013, I took an early flight to Atlanta, with a bit of a delay because of a faulty tractor in Charles de Gaulle airport but all in all an overall smooth trip. We alas flew too much south this time to get any view of Greenland except for the glimpse below… Apart from working on my slides for today’s lecture, I watched bits (actually most) of rather silly films, The Lone Ranger and Oblivion, not really worth reviewing here. (The former is playing too much on second degree references to Pirates of the Caribbean. From Johnny Depp making faces to his playing with his watch, to the recurrent madman wearing women’s clothes and playing with an umbrella. The second one was just appalling, from the abysmally poor acting to the ultimate absence of a plot…) I also read in The NYT about a new super-prize in Mathematics to be launched by a few “philanthropists”, including Mark Zuckerberg. The paper was not giving any detail on the focus of the prize and on the motives of the generous donators. Interestingly, the similar prize they set for physics went to two proponents of string theory, which is still a mathematical construct with no experimental evidence, as far as I understand…Rereading Johnson’s PNAS paper for my tutorial had the side result of making me realise him using a flat prior on a normal mean without more justification than there is a “constant factor that arises from the uniform distribution on μ”…
We received the good news from the Program Committee of the next ISBA World meeting in Cancún, Quintana Roo, México, that our proposal of a short course on ABC methods was accepted. So, along with Jean-Michel Marin, I hope to introduce ABC to a large group of interested participants on either July 13 or the morn of July 14. Here is the abstract for the short course
ABC appeared in 1999 to solve complex genetic problems where the likelihood of the model was impossible to compute. They are now a standard tool in the statistical genetic community but have also addressed many other problems where likelihood computation was also an issue, including dynamic models in signal processing and financial data analysis. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. Nonetheless, ABC techniques have several claims to validity: first, they are connected with econometric methods like indirect inference. Second, they can be expressed in terms of various non-parametric estimators of the likelihood or of the posterior density and follow standard convergence patterns. At last, they appear as regular Bayesian inference over noisy data. The lectures cover those validation steps but also detail the different implementations of ABC algorithms and the calibration of their parameters. The second part of the course illustrates those issues in the special case of the coalescent model used in population genetics, where many of the early advances of ABC were first implemented.
and the complete description is available on the ISBA website.
In addition, the special ISBA section sessions for BayesComp and O’Bayes ISBA sections have been accepted too. (As well as sessions for most of the other ISBA sections.) Thanks to Raquel Prado and to the whole scientific committee for working hard towards another successful ISBA World meeting! Note that the early bird conference registration begins today, so make sure to book your seat for Cancun!
I had a wonderful time in CMU, talking with a lot of faculty about their research (and mine), like reminiscing of things past and expanding on things to come with Larry (not to mention exchanging blogging impressions), giving my seminar talk, having a great risotto at Casbah, and a nice dinner at Legume, going for morning runs in the nearby park… One particularly memorable moment was the discussion I had with Jay as/since he went back to our diverging views about objective Bayes and improper priors, as expressed in the last chapter of his book and my review of it. While we kept disagreeing on their relevance and on whether or not they should be used, I had to concede that one primary reason for using reference priors is one of laziness in not seeking expert opinions. Even though there always is a limit to the information provided by such experts that means a default input at one level or the next (of a hierarchical model). Jay also told me of his proposal (as reported in his 1996 Bayesian methods and ethics in a clinical trial design book) for conducting clinical trials with several experts (with different priors) and sequentially weighting them by their predictive success. Proposal which made me think of a sequential way to compare models by their predictive abilities and still use improper priors…