Just got this announcement that MaxEnt 2013, 33ième du genre, is taking place in Canberra, Australia, next December. (Which is winter here but summer there!) See the website for details, although they are not yet aplenty! I took part in MaxEnt 2009, in Oxford, Mississipi, but will not attend MaxEnt 2013 as it is (far away and) during O-Bayes 2013 in Duke…
Archive for O’Bayes
MaxEnt 2013, Canberra, Dec. 15-20
Posted in Mountains, pictures, Statistics, Travel, University life with tags Australia, Canberra, conference, E.T. Jaynes, MaxEnt, maximum entropy, O'Bayes, Oxford (Mississipi) on July 3, 2013 by xi'anBayes 250 in Durham
Posted in Books, Statistics, Travel, University life, Wines with tags An Essay towards solving a Problem in the Doctrine of Chances, anniversary, conference, Duke University, Durham, EFab@, ISBA, O'Bayes, Sharon McGrayne, the theory that would not die, Thomas Bayes, USA, workshop on March 27, 2013 by xi'anReproducing an email from ISBA (sorry about the confusion purposely created by the title, this is Durham, North Carolina, not Durham, England, just as the London in Bayes 250 in London was London, England, not London, Ontario!):
ISBA announces a special celebration of the 250th anniversary of the presentation (December 23, 1763) of Thomas Bayes’ seminal paper “An Essay towards solving a Problem in the Doctrine of Chances” that will be held at Duke University in conjunction with the O-Bayes 13 Workshop (December 15-19) and EFab@ Bayes250 Workshop (December 15-17). (I am part of the scientific committee for O-Bayes 13!)
Speakers for the anniversary celebration are legendary contributors to the Bayesian literature, spanning a range of fields:
- Stephen Fienberg, Carnegie-Mellon University
- Michael Jordan, University of California, Berkeley
- Christopher Sims, Princeton University
- Adrian Smith, University of London
- Stephen Stigler, University of Chicago
There will be a banquet in the evening, with a speech by Sharon Bertsch McGrayne, noted author of the popular book “The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines and Emerged Triumphant From Two Centuries of Controversy.”
Error and Inference [end]
Posted in Books, Statistics, University life with tags Allan Birnbaum, book review, Error and Inference, Error-Statistical philosophy, foundations, Likelihood Principle, O'Bayes, philosophy of sciences, R.A. Fisher, statistical inference on October 11, 2011 by xi'an(This is my sixth and last post on Error and Inference, being as previously a raw and naïve reaction born from a linear and sluggish reading of the book, rather than a deeper and more informed criticism with philosophical bearings. Read at your own risk.)
“‘It is refreshing to see Cox and Mayo give a hard-nosed statement of what scientific objectivity demands of an account of statistics, show how it relates to frequentist statistics, and contrast that with the notion of “objectivity” used by O-Bayesians.”—A. Spanos, p.326, Error and Inference, 2010
In order to conclude my pedestrian traverse of Error and Inference, I read the discussion by Aris Spanos of the second part of the seventh chapter by David Cox’s and Deborah Mayo’s, discussed in the previous post. (In the train to the half-marathon to be precise, which may have added a sharper edge to the way I read it!) The first point in the discussion is that the above paper is “a harmonious blend of the Fisherian and N-P perspectives to weave a coherent frequentist inductive reasoning anchored firmly on error probabilities”(p.316). The discussion by Spanos is very much a-critical of the paper, so I will not engage into a criticism of the non-criticism, but rather expose some thoughts of mine that came from reading this apology. (Remarks about Bayesian inference are limited to some piques like the above, which only reiterates those found earlier [and later: “the various examples Bayesians employ to make their case involve some kind of “rigging” of the statistical model“, Aris Spanos, p.325; “The Bayesian epistemology literature is filled with shadows and illusions“, Clark Glymour, p. 335] in the book.) [I must add I do like the mention of O-Bayesians, as I coined the O’Bayes motto for the objective Bayes bi-annual meetings from 2003 onwards! It also reminds me of the O-rings and of the lack of proper statistical decision-making in the Challenger tragedy…]
The “general frequentist principle for inductive reasoning” (p.319) at the core of Cox and Mayo’s paper is obviously the central role of the p-value in “providing (strong) evidence against the null H0 (for a discrepancy from H0)”. Once again, I fail to see it as the epitome of a working principle in that
- it depends on the choice of a divergence d(z), which reduces the information brought by the data z;
- it does not articulate the level for labeling nor the consequences of finding a low p-value;
- it ignores the role of the alternative hypothesis.
Furthermore, Spanos’ discussion deals with “the fallacy of rejection” (pp.319-320) in a rather artificial (if common) way, namely by setting a buffer of discrepancy γ around the null hypothesis. While the choice of a maximal degree of precision sounds natural to me (in the sense that a given sample size should not allow for the discrimination between two arbitrary close values of the parameter), the fact that γ is in fine set by the data (so that the p-value is high) is fairly puzzling. If I understand correctly, the change from a p-value to a discrepancy γ is a fine device to make the “distance” from the null better understood, but it has an extremely limited range of application. If I do not understand correctly, the discrepancy γ is fixed by the statistician and then this sounds like an extreme form of prior selection.
There is at least one issue I do not understand in this part, namely the meaning of the severity evaluation probability
as the conditioning on the event seems impossible in a frequentist setting. This leads me to an idle and unrelated questioning as to whether there is a solution to
as this would be the ultimate discrepancy. Or whether this does not make any sense… because of the ambiguous role of z0, which needs somehow to be integrated out. (Otherwise, d can be chosen so that the probability is 1.)
“If one renounces the likelihood, the stopping rule, and the coherence principles, marginalizes the use of prior information as largely untrustworthy, and seek procedures with `good’ error probabilistic properties (whatever that means), what is left to render the inference Bayesian, apart from a belief (misguided in my view) that the only way to provide an evidential account of inference is to attach probabilities to hypotheses?”—A. Spanos, p.326, Error and Inference, 2010
The role of conditioning ancillary statistics is emphasized both in the paper and the discussion. This conditioning clearly reduces variability, however there is no reservation about the arbitrariness of such ancillary statistics. And the fact that conditioning any further would lead to conditioning upon the whole data, i.e. to a Bayesian solution. I also noted a curious lack of proper logical reasoning in the argument that, when
using the conditional ancillary distribution is enough, since, while “any departure from f(z|s) implies that the overall model is false” (p.322), but not the reverse. Hence, a poor choice of s may fail to detect a departure. (Besides the fact that fixed-dimension sufficient statistics do not exist outside exponential families.) Similarly, Spanos expands about the case of a minimal sufficient statistic that is independent from a maximal ancillary statistic, but such cases are quite rare and limited to exponential families [in the iid case]. Still in the conditioning category, he also supports Mayo’s argument against the likelihood principle being a consequence of the sufficiency and weak conditionality principles. A point I discussed in a previous post. However, he does not provide further evidence against Birnbaum’s result, arguing rather in favour of a conditional frequentist inference I have nothing to complain about. (I fail to perceive the appeal of the Welch uniform example in terms of the likelihood principle.)
In an overall conclusion, let me repeat and restate that this series of posts about Error and Inference is far from pretending at bringing a Bayesian reply to the philosophical arguments raised in the volume. The primary goal being of “taking some crucial steps towards legitimating the philosophy of frequentist statistics” (p.328), I should not feel overly concerned. It is only when the debate veered towards a comparison with the Bayesian approach [often too often of the “holier than thou” brand] that I felt allowed to put in my twopennies worth… I do hope I may crystallise this set of notes into a more constructed review of the book, if time allows, although I am pessimistic at the chances of getting it published given our current difficulties with the critical review of Murray Aitkin’s Statistical Inference. However, as a coincidence, we got back last weekend an encouraging reply from Statistics and Risk Modelling, prompting us towards a revision and the prospect of a reply by Murray.
Parallel computation [back]
Posted in R, Statistics, University life with tags Aussois, independent Metropolis-Hastings algorithm, JCGS, O'Bayes, parallel processing, R, Rao-Blackwellisation on February 13, 2011 by xi'an
We have now received reports back from JCGS for our parallel MCMC paper and they all are very nice and supportive! The reviewers essentially all like the Rao-Blackwellisation concept we developed in the paper and ask for additions towards a more concrete feeling for the practical consequences of the method. We should thus be able to manage a revision in the coming week or so. Especially because we have had further ideas about the extension of the method to regular Metropolis-Hastings algorithms like the random walk avatar. (The above picture is completely unrelated with the paper, but conveys some feeling of parallelism. I made it [in R] for the poster of the O’Bayes 03 meeting I organised in Aussois in 2003.)
Marginalisation paradoxes
Posted in Statistics with tags Bayesian statistics, improper prior, Jeffreys, O'Bayes, workshop on June 7, 2009 by xi'an
There was a poster by Timothy Wallstrom yesterday night at the O-Bayes09 poster session about marginalisation paradoxes and we had a nice chat about this topic. Marginalisation paradoxes are fascinating and I always mention them in my Bayesian class, because I think they illustrate the limitations of how much one can interpret an improper prior. There is a consequent literature on how to “solve” marginalisation paradoxes, following Jaynes’ comments on the foundational paper of David, Stone and Zidek (Journal of the Royal Statistical Society, 1974), but—and this is where I disagree with Timothy—I do not think they need to be “solved” either by uncovering the group action on the problem (left Haar versus right Haar) or by using different proper prior sequences. For me, the core of the “paradox” is that writing an improper prior as
does not imply that 
