Today I am flying to Austin, Texas, on the occasion of the O’Bayes 2017 conference, the 12th meeting in the series. In complete objectivity (I am a member of the scientific committee!), the scientific program looks quite exciting, with new themes and new faces. (And Peter Müller concocted a special social program as well!) As indicated above [with an innovative spelling of my first name!] I will give my “traditional” tutorial on O’Bayes testing and model choice tomorrow, flying back to Paris on Wednesday (and alas missing the final talks, including Better together by Pierre!). A nice pun is that the conference centre is located on Robert De[a]dman Drive, which I hope is not premonitory of a fatal ending to my talk there..!
Archive for objective Bayes
off to Austin!
Posted in Books, Kids, Statistics, Travel, University life, Wines with tags Austin, conference, ISBA, O'Bayes17, objective Bayes, Objective Bayesian hypothesis testing, Robert Dedman, Texas, The University of Texas at Austin, USA on December 9, 2017 by xi'anO’Bayes in action
Posted in Books, Kids, Statistics, University life with tags bois de Boulogne, Charles de Gaulle, invariance, Jeffreys priors, La Défense, mathematical puzzle, noninformative priors, O-Bayes 2017, objective Bayes, randomisation, RER B, Roissy, Université Paris Dauphine on November 7, 2017 by xi'an
My next-door colleague [at Dauphine] François Simenhaus shared a paradox [to be developed in an incoming test!] with Julien Stoehr and I last week, namely that, when selecting the largest number between a [observed] and b [unobserved], drawing a random boundary on a [meaning that a is chosen iff a is larger than this boundary] increases the probability to pick the largest number above ½2…
When thinking about it in the wretched RER train [train that got immobilised for at least two hours just a few minutes after I went through!, good luck to the passengers travelling to the airport…] to De Gaulle airport, I lost the argument: if a<b, the probability [for this random bound] to be larger than a and hence for selecting b is 1-Φ(a), while, if a>b, the probability [of winning] is Φ(a). Hence the only case when the probability is ½ is when a is the median of this random variable. But, when discussing the issue further with Julien, I exposed an interesting non-informative prior characterisation. Namely, if I assume a,b to be iid U(0,M) and set an improper prior 1/M on M, the conditional probability that b>a given a is ½. Furthermore, the posterior probability to pick the right [largest] number with François’s randomised rule is also ½, no matter what the distribution of the random boundary is. Now, the most surprising feature of this coffee room derivation is that these properties only hold for the prior 1/M. Any other power of M will induce an asymmetry between a and b. (The same properties hold when a,b are iid Exp(M).) Of course, this is not absolutely unexpected since 1/M is the invariant prior and since the “intuitive” symmetry only holds under this prior. Power to O’Bayes!
When discussing again the matter with François yesterday, I realised I had changed his wording of the puzzle. The original setting is one with two cards hiding the unknown numbers a and b and of a player picking one of the cards. If the player picks a card at random, there is indeed a probability of ½ of picking the largest number. If the decision to switch or not depends on an independent random draw being larger or smaller than the number on the observed card, the probability to get max(a,b) in the end hits 1 when this random draw falls into (a,b) and remains ½ outside (a,b). Randomisation pays.
Bayesian spectacles
Posted in Books, pictures, Statistics, University life with tags Amsterdam, Bayes factors, Bayesian Spectacles, blogging, Holland, JASP, non-informative priors, objective Bayes, reference priors, UMPBTs, uniformly most powerful tests, University of Amsterdam on October 4, 2017 by xi'anE.J. Wagenmakers and his enthusiastic team of collaborators at University of Amsterdam and in the JASP software designing team have started a blog called Bayesian spectacles which I find a fantastic title. And not only because I wear glasses. Plus, they got their own illustrator, Viktor Beekman, which sounds like the epitome of sophistication! (Compared with resorting to vacation or cat pictures…)
In a most recent post they addressed the criticisms we made of the 72 author paper on p-values, one of the co-authors being E.J.! Andrew already re-addressed some of the address, but here is a disagreement he let me to chew on my own [and where the Abandoners are us!]:
Disagreement 2. The Abandoners’ critique the UMPBTs –the uniformly most powerful Bayesian tests– that features in the original paper. This is their right (see also the discussion of the 2013 Valen Johnson PNAS paper), but they ignore the fact that the original paper presented a series of other procedures that all point to the same conclusion: p-just-below-.05 results are evidentially weak. For instance, a cartoon on the JASP blog explains the Vovk-Sellke bound. A similar result is obtained using the upper bounds discussed in Berger & Sellke (1987) and Edwards, Lindman, & Savage (1963). We suspect that the Abandoners’ dislike of Bayes factors (and perhaps their upper bounds) is driven by a disdain for the point-null hypothesis. That is understandable, but the two critiques should not be mixed up. The first question is Given that we wish to test a point-null hypothesis, do the Bayes factor upper bounds demonstrate that the evidence is weak for p-just-below-.05 results? We believe they do, and in this series of blog posts we have provided concrete demonstrations.
Obviously, this reply calls for an examination of the entire BS blog series, but being short in time at the moment, let me point out that the upper lower bounds on the Bayes factors showing much more support for H⁰ than a p-value at 0.05 only occur in special circumstances. Even though I spend some time in my book discussing those bounds. Indeed, the [interesting] fact that the lower bounds are larger than the p-values does not hold in full generality. Moving to a two-dimensional normal with potentially zero mean is enough to see the order between lower bound and p-value reverse, as I found [quite] a while ago when trying to expand Berger and Sellker (1987, the same year as I was visiting Purdue where both had a position). I am not sure this feature has been much explored in the literature, I did not pursue it when I realised the gap was missing in larger dimensions… I must also point out I do not have the same repulsion for point nulls as Andrew! While considering whether a parameter, say a mean, is exactly zero [or three or whatever] sounds rather absurd when faced with the strata of uncertainty about models, data, procedures, &tc.—even in theoretical physics!—, comparing several [and all wrong!] models with or without some parameters for later use still makes sense. And my reluctance in using Bayes factors does not stem from an opposition to comparing models or from the procedure itself, which is quite appealing within a Bayesian framework [thus appealing per se!], but rather from the unfortunate impact of the prior [and its tail behaviour] on the quantity and on the delicate calibration of the thing. And on a lack of reference solution [to avoid the O and the N words!]. As exposed in the demise papers. (Which main version remains in a publishing limbo, the onslaught from the referees proving just too much for me!)
OBayes 17 travel support
Posted in Statistics with tags Austin, conference, funding, ISBA, new researchers, O'Bayes17, objective Bayes, Texas, The University of Texas at Austin, travel grant on September 1, 2017 by xi'an
The OBayes 17 conference in Austin, Texas, next December is getting nearer! This post is to advertise for the availability of a dozen travel grants for junior investigators, as detailed on the webpage of the conference. One of those grants will even become an ISBA New Researchers Travel Award for the event! This comes on top of registration and accommodation being quite reasonable, thanks to Peter Mueller’s efforts, and hence makes this conference most affordable and attractive for young researchers. Apply now!!!
objective and subjective RSS Read Paper next week
Posted in Books, pictures, Statistics, Travel, University life, Wines with tags Andrew Gelman, Christian Hennig, discussion paper, England, frequentist inference, London, objective Bayes, objectivism, Philosophy of Science, Read paper, Royal Statistical Society, RSS, Series A, subjective versus objective Bayes, subjectivity on April 5, 2017 by xi'an
Andrew Gelman and Christian Hennig will give a Read Paper presentation next Wednesday, April 12, 5pm, at the Royal Statistical Society, London, on their paper “Beyond subjective and objective in statistics“. Which I hope to attend and else to write a discussion. Since the discussion (to published in Series A) is open to everyone, I strongly encourage ‘Og’s readers to take a look at the paper and the “radical” views therein to hopefully contribute to this discussion. Either as a written discussion or as comments on this very post.
