meet the black heart of Messier

the explanation why Science gets underfunded

round-table on Bayes[ian[ism]]

In a [sort of] coincidence, shortly after writing my review on Le bayésianisme aujourd’hui, I got invited by the book editor, Isabelle Drouet, to take part in a round-table on Bayesianism in La Sorbonne. Which constituted the first seminar in the monthly series of the séminaire “Probabilités, Décision, Incertitude”. Invitation that I accepted and honoured by taking place in this public debate (if not dispute) on all [or most] things Bayes. Along with Paul Egré (CNRS, Institut Jean Nicod) and Pascal Pernot (CNRS, Laboratoire de chimie physique). And without a neuroscientist, who could not or would not attend.

While nothing earthshaking came out of the seminar, and certainly not from me!, it was interesting to hear of the perspectives of my philosophy+psychology and chemistry colleagues, the former explaining his path from classical to Bayesian testing—while mentioning trying to read the book Statistical rethinking I  reviewed a few months ago—and the later the difficulty to teach both colleagues and students the need for an assessment of uncertainty in measurements. And alluding to GUM, developed by the Bureau International des Poids et Mesures I visited last year. I tried to present my relativity viewpoints on the [relative] nature of the prior, to avoid the usual morass of debates on the nature and subjectivity of the prior, tried to explain Bayesian posteriors via ABC, mentioned examples from The Theorem that Would not Die, yet untranslated into French, and expressed reserves about the glorious future of Bayesian statistics as we know it. This seminar was fairly enjoyable, with none of the stress induced by the constraints of a radio-show. Just too bad it did not attract a wider audience!

le bayésianisme aujourd’hui [book review]

It is quite rare to see a book published in French about Bayesian statistics and even rarer to find one that connects philosophy of science, foundations of probability, statistics, and applications in neurosciences and artificial intelligence. Le bayésianisme aujourd’hui (Bayesianism today) was edited by Isabelle Drouet, a Reader in Philosophy at La Sorbonne. And includes a chapter of mine on the basics of Bayesian inference (à la Bayesian Choice), written in French like the rest of the book.

The title of the book is rather surprising (to me) as I had never heard the term Bayesianism mentioned before. As shown by this link, the term apparently exists. (Even though I dislike the sound of it!) The notion is one of a probabilistic structure of knowledge and learning, à la Poincaré. As described in the beginning of the book. But I fear the arguments minimising the subjectivity of the Bayesian approach should not be advanced, following my new stance on the relativity of probabilistic statements, if only because they are defensive and open the path all too easily to counterarguments. Similarly, the argument according to which the “Big Data” era makesp the impact of the prior negligible and paradoxically justifies the use of Bayesian methods is limited to the case of little Big Data, i.e., when the observations are more or less iid with a limited number of parameters. Not when the number of parameters explodes. Another set of arguments that I find both more modern and compelling [for being modern is not necessarily a plus!] is the ease with which the Bayesian framework allows for integrative and cooperative learning. Along with its ultimate modularity, since each component of the learning mechanism can be extracted and replaced with an alternative.

relativity is the keyword

As I was teaching my introduction to Bayesian Statistics this morning, ending up with the chapter on tests of hypotheses, I found reflecting [out loud] on the relative nature of posterior quantities. Just like when I introduced the role of priors in Bayesian analysis the day before, I stressed the relativity of quantities coming out of the BBB [Big Bayesian Black Box], namely that whatever happens as a Bayesian procedure is to be understood, scaled, and relativised against the prior equivalent, i.e., that the reference measure or gauge is the prior. This is sort of obvious, clearly, but bringing the argument forward from the start avoids all sorts of misunderstanding and disagreement, in that it excludes the claims of absolute and certainty that may come with the production of a posterior distribution. It also removes the endless debate about the determination of the prior, by making each prior a reference on its own. With an additional possibility of calibration by simulation under the assumed model. Or an alternative. Again nothing new there, but I got rather excited by this presentation choice, as it seems to clarify the path to Bayesian modelling and avoid misapprehensions.

Further, the curious case of the Bayes factor (or of the posterior probability) could possibly be resolved most satisfactorily in this framework, as the [dreaded] dependence on the model prior probabilities then becomes a matter of relativity! Those posterior probabilities depend directly and almost linearly on the prior probabilities, but they should not be interpreted in an absolute sense as the ultimate and unique probability of the hypothesis (which anyway does not mean anything in terms of the observed experiment). In other words, this posterior probability does not need to be scaled against a U(0,1) distribution. Or against the p-value if anyone wishes to do so. By the end of the lecture, I was even wondering [not so loudly] whether or not this perspective was allowing for a resolution of the Lindley-Jeffreys paradox, as the resulting number could be set relative to the choice of the [arbitrary] normalising constant.