Next May 1-3, I will attend the 4th Bayesian, Fiducial and Frequentist Conference at Harvard University (hopefully not under snow at that time of year), which is a meeting between philosophers and statisticians about foundational thinking in statistics and inference under uncertainty. This should be fun! (Registration is now open.)
Archive for Cambridge
A love letter from some Europeans against Brexit that appeared in the Times Literary Supplement a few days ago, and which message I definitely support:
All of us in Europe respect the right of the British people to decide whether they wish to remain with us in the European Union. It is your decision, and we will all accept it. Nevertheless, if it will help the undecided to make up their minds, we would like to express how very much we value having the United Kingdom in the European Union. It is not just treaties that join us to your country, but bonds of admiration and affection. All of us hope that you will vote to renew them. Britain, please stay.
As in Bristol two months ago, where I joined the statistics reading in the morning, I had the opportunity to discuss the paper on testing via mixtures prior to my talk with a group of Harvard graduate students. Which concentrated on the biasing effect of the Bayes factor against the more complex hypothesis/model. Arguing [if not in those terms!] that Occam’s razor was too sharp. With a neat remark that decomposing the log Bayes factor as
meant that the first marginal was immensely and uniquely impacted by the prior modelling, hence very likely to be very small for a larger model H, which would then take forever to recover from. And asking why there was such a difference with cross-validation
where the leave-one out posterior predictor is indeed more stable. While the later leads to major overfitting in my opinion, I never spotted the former decomposition which does appear as a strong and maybe damning criticism of the Bayes factor in terms of long-term impact of the prior modelling.
Other points made during the talk or before when preparing the talk:
- additive mixtures are but one encompassing model, geometric mixtures could be fun too, if harder to process (e.g., missing normalising constant). Or Zellner’s mixtures (with again the normalising issue);
- if the final outcome of the “test” is the posterior on α itself, the impact of the hyper-parameter on α is quite relative since this posterior can be calibrated by simulation against limiting cases (α=0,1);
- for the same reason the different rate of accumulation near zero and one when compared with a posterior probability is hardly worrying;
- what I see as a fundamental difference in processing improper priors for Bayes factors versus mixtures is not perceived as such by everyone;
- even a common parameter θ on both models does not mean both models are equally weighted a priori, which relates to an earlier remark in Amsterdam about the different Jeffreys priors one can use;
- the MCMC output also produces a sample of θ’s which behaviour is obviously different from single model outputs. It would be interesting to study further the behaviour of those samples, which are not to be confused with model averaging;
- the mixture setting has nothing intrinsically Bayesian in that the model can be processed in other ways.
Next week, I will be in Harvard Monday and Tuesday, visiting friends in the Department of Statistics and giving a seminar. The slides for the talk will be quite similar to those of my talk in Bristol, a few weeks ago. Hopefully, there will not be too much overlap between both audiences! And hopefully I’ll manage to get to my conclusion before all hell breaks loose (which is why I strategically set my conclusion in the early slides!)
In connection with Dawkins’ The God delusion, which review is soon to appear on the ‘Og, a poster at an exhibit on evolution in the Harvard Museum of Natural History, which illustrates one of Dawkins’ points on scientific agosticism. Namely, that refusing to take a stand on the logical and philosophical opposition between science and religion(s) is not a scientific position. The last sentence in the poster is thus worse than unnecessary…