Dennis Lindley most sadly passed away yesterday at the hospital near his home in Somerset. He was one of the founding fathers of our field (of Bayesian statistics), who contributed to formalise Bayesian statistics in a coherent theory. And to make it one with rational decision-making, a perspective missing in Jeffreys’ vision. (His papers figured prominently in the tutorials we gave yesterday for the opening of O’Bayes 250.) At the age of 90, his interest in the topic had not waned away: as his interview with Tony O’Hagan last Spring showed, his passionate arguing for the rationale of the Bayesian approach was still there and alive! The review he wrote of The Black Swan a few years ago also demonstrated he had preserved his ability to see through bogus arguments. (See his scathing “One hardly advances the respect with which statisticians are held in society by making such declarations” in his ripping discussion of Aitkin’s 1991 Posterior Bayes factors.) He also started this interesting discussion last year about the five standard deviations “needed” for the Higgs boson… My personal email contacts with Dennis over the re-reading of Jeffreys’ book were a fantastic experience as he kindly contributed by expanding on how the book was received at the time and correcting some of my misunderstanding. It is a pity I can no longer send him the (soon to come?) final version of my Jeffreys-Lindley paradox paper as I intended to do. The email email@example.com will no longer answer our queries… I figure there will be many testimonies and shared memories of his contributions and life at the Bayes-250 conference tomorrow. Farewell, Dennis, and I hope you now explore the paths of a more coherent world than ours!
Archive for Thomas Bayes
When visiting the bookstore on the campus of the University of Warwick two weeks ago, I spotted this book, Philosophy of Science, a very short introduction, by Samir Okasha, and the “bargain” offer of getting two books for £10 enticed me to buy it along with a Friedrich Nietzsche, a very short introduction… (Maybe with the irrational hope that my daughter would take a look at those for her philosophy course this year!)
“Popper’s attempt to show that science can get by without induction does not succeed.” (p.23)
Since this is [unsusrprisingly!] a very short introduction, I did not get much added value from the book. Nonetheless, it was an easy read for short trips in the metro and short waits here and there. And would be a good [very short] introduction to any one newly interested in the philosophy of sciences. The first chapter tries to define what science is, with reference to the authority of Popper (and a mere mention of Wittgenstein), and concludes that there is no clear-cut demarcation between science and pseudo-science. (Mathematics apparently does not constitute a science: “Physics is the most fundamental science of all”, p.55) I would have liked to see the quote from Friedrich Nietzsche
“It is perhaps just dawning on five or six minds that physics, too, is only an interpretation and exegesis of the world (to suit us, if I may say so!) and not a world-explanation.”
in Beyond Good and Evil. as it illustrates the main point of the chapter and maybe the book that scientific theories can never be proven true, Plus, it is often misinterpreted as a anti-science statement by Nietzsche. (Plus, it links both books I bought!) Continue reading
A few weeks ago, Larry Wasserman posted on Normal Deviate an entry on noninformative priors as a lost cause for statistics. I first reacted rather angrily to this post, then decided against posting my reply. After a relaxing week in Budapest, and the prospect of the incoming summer break, I went back to the post and edited it towards more constructive goals… The post also got discussed by Andrew and Entsophy, generating in each case a heap of heated discussions. (Enjoy your summer, winter is coming!)
Although Larry wrote he wanted to restrain from only posting on Bayesian statistics, he does seem attracted to them like a moth to a candle… This time, it is about the “lost cause of noninformative priors”. While Larry is 200% entitled to post about whatever he likes or dislikes, the post does not really bring new fuel to the debate, if debate there is. First, I think everyone agrees that there is no such thing as a noninformative prior or a prior representing ignorance. (To quote from Jeffreys: “A prior probability used to express ignorance is merely the formal statement of ignorance” (ToP, VIII, x8.1). Every prior brings something into the game and this is reflected in the posterior inference. Sometimes, the impact is enormous and we may be unaware of it. Take for instance Bayesian nonparametrics. It is thus essential to keep this in mind. (And to keep calm!) Which does not mean we should not use them. Indeed, noninformative priors are a way of setting a reference measure, from which one can start evaluating the impact of picking this or that prior. Just a measure. (No-one gets emotional when hearing the Lebesgue measure mentioned, right?!) And if the reference prior is a σ-finite measure, one cannot even put a meaning to events like θ>0. This reference measure is required to set the Bayesian crank turning, here or there depending on one’s prior beliefs or information. If we reject those reference priors for accepting only the cases when the prior is provided along with the data and the model, I think everyone is a Bayesian. Even Feller. Even Larry (?).
Second, there is alas too much pathos or unintended meaning put in names like noninformative, ignorance, objective, &tc. And this may be the major message in Larry’s post. We should call those reference priors Linear A priors in reference to the mostly undeciphered Minoan alphabet. Or whatever name with no emotional content whatsoever in order not to drive people crazy. Noninformative is not even a word, to start with… And I dunno how to define ignorance in a mathematical manner.Once more in connection with the EMS 2013 meeting in Budapest, I do not see why one should object more to reference priors than to the so-called “subjective” priors, as the former provide a baseline against which to test the latter, using e.g. Xiao Li’s approach. I am actually much more annoyed by the use of a specific proper prior in a statistical analysis when this prior is neither justified nor assessed in terms of robustness. And I see nothing wrong in establishing either asymptotic or frequentist properties about some procedures connected with some of those reference priors: I became a Bayesian this way, after all.
Anyway, have a nice (end of the) summer if you are in the Northern Hemisphere, and expect delays (or snapshots!) on the ‘Og for the coming fortnight…
Last day at EMS 2013! I started the day with an attempt to run inside the big necropolis on the east of town (Nemzeti sirkert), attempt that failed as I was too early. I then delivered my ISBA Thomas Bayes memorial lecture, with an amazing number of people (amazing conditional on the fact that it was delivered at 9am the morning after the banquet, on the last day of the conference, that it was a memorial historical talk which could be (mis-)perceived as Bayesian propaganda, and that I had put my slides on line already!). I managed (in I hope a comprehensible and not-too-boring way!) to cover most of the slides, skipping some ABC details, in the allotted hour, and not forgetting the historical note (Teller was born here) and the local ABC picture… Many aspects of past and current Bayesian statistics were missing: Fabrizio Ruggeri pointed out prior elicitation and Xiao-Li Meng [who wore a special tie with Thomas Bayes' picture!] George Box. As an aside, has anyone versed in image analysis ever tried to link Thomas Bayes somehow doubtful portrait with his father’s? They do not look the least related to my unexpert eyes…
The rest of the day went very quickly, with a Bayesian computation session on SMC and exact approximations, and an afternoon consisting of Larry Brown’s talk on linear models as approximations (bringing a new light on the topic!) and of Xiao-Li Meng’s talk on measuring the impact of priors through a new information device. While I attended the “Future of Statistics” panel like most of the remaining participants, the future remained rather foggy, as I could not make my mind between the optimist side pointed out the growing need of statisticians at every level and the pessimist view that those jobs were mostly taken by poorly trained non-statisticians… In conclusion, I enjoyed the meeting for its diversity and range of talks, as well as its fantastic location of course!