speed seminar-ing

Yesterday, I  made a quick afternoon trip to Montpellier as replacement of a seminar speaker who had cancelled at the last minute. Most obviously, I gave a talk about our “testing as mixture” proposal. And as previously, the talk generated a fair amount of discussion and feedback from the audience. Providing me with additional aspects to include in a revision of the paper. Whether or not the current submission is rejected, new points made and received during those seminars will have to get in a revised version as they definitely add to the appeal to the perspective. In that seminar, most of the discussion concentrated on the connection with decisions based on such a tool as the posterior distribution of the mixture weight(s). My argument for sticking with the posterior rather than providing a hard decision rule was that the message is indeed in arguing hard rules that end up mimicking the p- or b-values. And the catastrophic consequences of fishing for significance and the like. Producing instead a validation by simulating under each model pseudo-samples shows what to expect for each model under comparison. The argument did not really convince Jean-Michel Marin, I am afraid! Another point he raised was that we could instead use a distribution on α with support {0,1}, to avoid the encompassing model he felt was too far from the original models. However, this leads back to the Bayes factor as the weights in 0 and 1 are the marginal likelihoods, nothing more. However, this perspective on the classical approach has at least the appeal of completely validating the use of improper priors on common (nuisance or not) parameters. Pierre Pudlo also wondered why we could not conduct an analysis on the mixture of the likelihoods. Instead of the likelihood of the mixture. My first answer was that there was not enough information in the data for estimating the weight(s). A few more seconds of reflection led me to the further argument that the posterior on α with support (0,1) would then be a mixture of Be(2,1) and Be(1,2) with weights the marginal likelihoods, again (under a uniform prior on α). So indeed not much to gain. A last point we discussed was the case of the evolution trees we analyse with population geneticists from the neighbourhood (and with ABC). Jean-Michel’s argument was that the scenari under comparison were not compatible with a mixture, the models being exclusive. My reply involved an admixture model that contained all scenarios as special cases. After a longer pondering, I think his objection was more about the non iid nature of the data. But the admixture construction remains valid. And makes a very strong case in favour of our approach, I believe.

After the seminar, Christian Lavergne and Jean-Michel had organised a doubly exceptional wine-and-cheese party: first because it is not usually the case there is such a post-seminar party and second because they had chosen a terrific series of wines from the Mas Bruguière (Pic Saint-Loup) vineyards. Ending up with a great 2007 L’Arbouse. Perfect ending for an exciting day. (I am not even mentioning a special Livarot from close to my home-town!)