Archive for Biometrika

revisiting marginalisation paradoxes [Bayesian reads #1]

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , on February 8, 2019 by xi'an

As a reading suggestion for my (last) OxWaSP Bayesian course at Oxford, I included the classic 1973 Marginalisation paradoxes by Phil Dawid, Mervyn Stone [whom I met when visiting UCL in 1992 since he was sharing an office with my friend Costas Goutis], and Jim Zidek. Paper that also appears in my (recent) slides as an exercise. And has been discussed many times on this  ‘Og.

Reading the paper in the train to Oxford was quite pleasant, with a few discoveries like an interesting pike at Fraser’s structural (crypto-fiducial?!) distributions that “do not need Bayesian improper priors to fall into the same paradoxes”. And a most fascinating if surprising inclusion of the Box-Müller random generator in an argument, something of a precursor to perfect sampling (?). And a clear declaration that (right-Haar) invariant priors are at the source of the resolution of the paradox. With a much less clear notion of “un-Bayesian priors” as those leading to a paradox. Especially when the authors exhibit a red herring where the paradox cannot disappear, no matter what the prior is. Rich discussion (with none of the current 400 word length constraint), including the suggestion of neutral points, namely those that do identify a posterior, whatever that means. Funny conclusion, as well:

“In Stone and Dawid’s Biometrika paper, B1 promised never to use improper priors again. That resolution was short-lived and let us hope that these two blinkered Bayesians will find a way out of their present confusion and make another comeback.” D.J. Bartholomew (LSE)

and another

“An eminent Oxford statistician with decidedly mathematical inclinations once remarked to me that he was in favour of Bayesian theory because it made statisticians learn about Haar measure.” A.D. McLaren (Glasgow)

and yet another

“The fundamentals of statistical inference lie beneath a sea of mathematics and scientific opinion that is polluted with red herrings, not all spawned by Bayesians of course.” G.N. Wilkinson (Rothamsted Station)

Lindley’s discussion is more serious if not unkind. Dennis Lindley essentially follows the lead of the authors to conclude that “improper priors must go”. To the point of retracting what was written in his book! Although concluding about the consequences for standard statistics, since they allow for admissible procedures that are associated with improper priors. If the later must go, the former must go as well!!! (A bit of sophistry involved in this argument…) Efron’s point is more constructive in this regard since he recalls the dangers of using proper priors with huge variance. And the little hope one can hold about having a prior that is uninformative in every dimension. (A point much more blatantly expressed by Dickey mocking “magic unique prior distributions”.) And Dempster points out even more clearly that the fundamental difficulty with these paradoxes is that the prior marginal does not exist. Don Fraser may be the most brutal discussant of all, stating that the paradoxes are not new and that “the conclusions are erroneous or unfounded”. Also complaining about Lindley’s review of his book [suggesting prior integration could save the day] in Biometrika, where he was not allowed a rejoinder. It reflects on the then intense opposition between Bayesians and fiducialist Fisherians. (Funny enough, given the place of these marginalisation paradoxes in his book, I was mistakenly convinced that Jaynes was one of the discussants of this historical paper. He is mentioned in the reply by the authors.)

the paper where you are a node

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on February 5, 2019 by xi'an

Sophie Donnet pointed out to me this arXived paper by Tianxi Li, Elizaveta Levina, and Ji Zhu, on a network resampling strategy for X validation, where I appear as a datapoint rather than as a [direct] citation! Which reminded me of the “where you are the hero” gamebooks with which my kids briefly played, before computer games took over. The model selection method is illustrated on a dataset made of X citations [reduced to 706 authors]  in all papers published between 2003 and 2012 in the Annals of Statistics, Biometrika, JASA, and JRSS Series B. With the outcome being the determination of a number of communities, 20, which the authors labelled as they wanted, based on 10 authors with the largest number of citations in the category. As it happens, I appear in the list, within the “mixed (causality + theory + Bayesian)” category (!), along with Jamie Robbins, Paul Fearnhead, Gilles Blanchard, Zhiqiang Tan, Stijn Vansteelandt, Nancy Reid, Jae Kwang Kim, Tyler VanderWeele, and Scott Sisson, which is somewhat mind-boggling in that I am pretty sure I never quoted six of these authors [although I find it hilarious that Jamie appears in the category, given that we almost got into a car crash together, at one of the Valencià meetings!].

Nature Outlook on AI

Posted in Statistics with tags , , , , , , , , , , , , , , , on January 13, 2019 by xi'an

The 29 November 2018 issue of Nature had a series of papers on AIs (in its Outlook section). At the general public (awareness) level than in-depth machine-learning article. Including one on the forecasted consequences of ever-growing automation on jobs, quoting from a 2013 paper by Carl Frey and Michael Osborne [of probabilistic numerics fame!] that up to 47% of US jobs could become automated. The paper is inconclusive on how taxations could help in or deter from transfering jobs to other branches, although mentioning the cascading effect of taxing labour and subsidizing capital. Another article covers the progresses in digital government, with Estonia as a role model, including the risks of hacking (but not mentioning Russia’s state driven attacks). Differential privacy is discussed as a way to keep data “secure” (but not cryptography à la Louis Aslett!). With another surprising entry that COBOL is still in use in some administrative systems. Followed by a paper on the apparently limited impact of digital technologies on mental health, despite the advertising efforts of big tech companies being described as a “race to the bottom of the brain stem”! And another one on (overblown) public expectations on AIs, although the New York Time had an entry yesterday on people in Arizona attacking self-driving cars with stones and pipes… Plus a paper on the growing difficulties of saving online documents and culture for the future (although saving all tweets ever published does not sound like a major priority to me!).

Interesting (?) aside, the same issue contains a general public article on the use of AIs for peer reviews (of submitted papers). The claim being that “peer review by artificial intelligence (AI) is promising to improve the process, boost the quality of published papers — and save reviewers time.” A wee bit over-optimistic, I would say, as the developed AI’s are at best “that statistics and methods in manuscripts are sound”. For instance, producing “key concepts to summarize what the paper is about” is not particularly useful. A degree of innovation compared with the existing would be. Or an automated way to adapt the paper style to the strict and somewhat elusive Biometrika style!

peer reviews on-line or peer community?

Posted in Statistics with tags , , , , , , , , , on September 20, 2018 by xi'an

Nature (or more precisely some researchers through Nature, associated with the UK Wellcome Trust, the US Howard Hughes Medical Institute (hhmo), and ASAPbio) has (have) launched a call for publishing reviews next to accept papers, one way or another, which is something I (and many others) have supported for quite a while. Including for rejected papers, not only because making these reviews public diminishes on principle the time involved in re-reviewing re-submitted papers but also because this should induce authors to revise papers with obvious flaws and missing references (?). Or abstain from re-submitting. Or publish a rejoinder addressing the criticisms. Anything that increases the communication between all parties, as well as the perspectives on a given paper. (This year, NIPS allows for the posting of reviews of rejected submissions, which I find a positive trend!)

In connection with this entry, I am still most sorry that I could not pursue the [superior in my opinion] project of Peer Community in computational statistics, for the time requested by Biometrika editing is just too important [given my current stamina!] for me to handle another journal (or the better alternative to a journal!). I hope someone else can take over the project and create the editorial team needed to run it.

And yet again in connection with this post (!), Andrew posted an announcement about the launch of res3archers.one, an on-line publication forum launched by Harry Crane and Ryan Martin, where the authors handle the peer review process from A to Z, including choosing the reviewers, whose reviews may be public or not, taken into account or not. Once published, the papers are open to comments from users, which constitutes a form of post-publication peer-review. Albeit a weak one in my opinion as the weakness of all such open depositories is the potential lack of interest of and reaction from the community. Incidentally, there is a $10 fee per submission for maintenance. Contrary to Peer Community in… the copyright is partly transferred to res3archers.one, which apparently prevents further publication in another journal.

asymptotic properties of ABC now appeared

Posted in Books, Statistics, University life with tags , , , , , , on September 1, 2018 by xi'an

Our paper with David Frazier, Gael Martin and Judith Rousseau has appeared in print in Biometrika, Volume 105, Issue 3, 1 September 2018, Pages 593–607, almost exactly two years after it was submitted. I am quite glad with the final version, though, and grateful for the editorial input, as the paper clearly characterises the connection between the tolerance level ε and the convergence rate of the summary statistic to its parameter identifying asymptotic mean. Asymptotic in the sample size, that is.

ABC’ptotics on-line

Posted in Statistics with tags , , , , , , , on June 14, 2018 by xi'an

Our paper on Asymptotic properties of ABC with David Frazier, Gael Martin, and Judith Rousseau, is now on-line on the Biometrika webpage. Coincidentally both papers by Wentao Li and Paul Fearnhead on ABC’ptotics are published in the June issue of the journal.

Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

approximate Bayesian inference under informative sampling

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , on March 30, 2018 by xi'an

In the first issue of this year Biometrika, I spotted a paper with the above title, written by Wang, Kim, and Yang, and thought it was a particular case of ABC. However, when I read it on a rare metro ride to Dauphine, thanks to my hurting knee!, I got increasingly disappointed as the contents had nothing to do with ABC. The purpose of the paper was to derive a consistent and convergent posterior distribution based on a estimator of the parameter θ that is… consistent and convergent under informative sampling. Using for instance a Normal approximation to the sampling distribution of this estimator. Or to the sampling distribution of the pseudo-score function, S(θ) [which pseudo-normality reminded me of Ron Gallant’s approximations and of my comments on them]. The paper then considers a generalisation to the case of estimating equations, U(θ), which may again enjoy a Normal asymptotic distribution. Involving an object that does not make direct Bayesian sense, namely the posterior of the parameter θ given U(θ)…. (The algorithm proposed to generate from this posterior (8) is also a mystery.) Since the approach requires consistent estimators to start with and aims at reproducing frequentist coverage properties, I am thus at a loss as to why this pseudo-Bayesian framework is adopted.