Archive for Thomas Bayes

carrer de Thomas Bayes [formulas magistrales]

Posted in pictures, Statistics, Travel with tags , , , , on June 11, 2015 by xi'an

carrer

eliminating an important obstacle to creative thinking: statistics…

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , on March 12, 2015 by xi'an

“We hope and anticipate that banning the NHSTP will have the effect of increasing the quality of submitted manuscripts by liberating authors from the stultified structure of NHSTP thinking thereby eliminating an important obstacle to creative thinking.”

About a month ago, David Trafimow and Michael Marks, the current editors of the journal Basic and Applied Social Psychology published an editorial banning all null hypothesis significance testing procedures (acronym-ed into the ugly NHSTP which sounds like a particularly nasty venereal disease!) from papers published by the journal. My first reaction was “Great! This will bring more substance to the papers by preventing significance fishing and undisclosed multiple testing! Power to the statisticians!” However, after reading the said editorial, I realised it was inspired by a nihilistic anti-statistical stance, backed by an apparent lack of understanding of the nature of statistical inference, rather than a call for saner and safer statistical practice. The editors most clearly state that inferential statistical procedures are no longer needed to publish in the journal, only “strong descriptive statistics”. Maybe to keep in tune with the “Basic” in the name of the journal!

“In the NHSTP, the problem is in traversing the distance from the probability of the finding, given the null hypothesis, to the probability of the null hypothesis, given the finding. Regarding confidence intervals, the problem is that, for example, a 95% confidence interval does not indicate that the parameter of interest has a 95% probability of being within the interval.”

The above quote could be a motivation for a Bayesian approach to the testing problem, a revolutionary stance for journal editors!, but it only illustrate that the editors wish for a procedure that would eliminate the uncertainty inherent to statistical inference, i.e., to decision making under… erm, uncertainty: “The state of the art remains uncertain.” To fail to separate significance from certainty is fairly appalling from an epistemological perspective and should be a case for impeachment, were any such thing to exist for a journal board. This means the editors cannot distinguish data from parameter and model from reality! Even more fundamentally, to bar statistical procedures from being used in a scientific study is nothing short of reactionary. While encouraging the inclusion of data is a step forward, restricting the validation or in-validation of hypotheses to gazing at descriptive statistics is many steps backward and does completely jeopardize the academic reputation of the journal, which editorial may end up being the last quoted paper. Is deconstruction now reaching psychology journals?! To quote from a critic of this approach, “Thus, the general weaknesses of the deconstructive enterprise become self-justifying. With such an approach I am indeed not sympathetic.” (Searle, 1983).

“The usual problem with Bayesian procedures is that they depend on some sort of Laplacian assumption to generate numbers where none exist (…) With respect to Bayesian procedures, we reserve the right to make case-by-case judgments, and thus Bayesian procedures are neither required nor banned from BASP.”

The section of Bayesian approaches is trying to be sympathetic to the Bayesian paradigm but again reflects upon the poor understanding of the authors. By “Laplacian assumption”, they mean Laplace´s Principle of Indifference, i.e., the use of uniform priors, which is not seriously considered as a sound principle since the mid-1930’s. Except maybe in recent papers of Trafimow. I also love the notion of “generat[ing] numbers when none exist”, as if the prior distribution had to be grounded in some physical reality! Although it is meaningless, it has some poetic value… (Plus, bringing Popper and Fisher to the rescue sounds like shooting Bayes himself in the foot.)  At least, the fact that the editors will consider Bayesian papers in a case-by-case basis indicate they may engage in a subjective Bayesian analysis of each paper rather than using an automated p-value against the 100% rejection bound!

[Note: this entry was suggested by Alexandra Schmidt, current ISBA President, towards an incoming column on this decision of Basic and Applied Social Psychology for the ISBA Bulletin.]

 

interesting mis-quote

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , on September 25, 2014 by xi'an

At a recent conference on Big Data, one speaker mentioned this quote from Peter Norvig, the director of research at Google:

“All models are wrong, and increasingly you can succeed without them.”

quote that I found rather shocking, esp. when considering the amount of modelling behind Google tools. And coming from someone citing Kernel Methods for Pattern Analysis by Shawe-Taylor and Christianini as one of his favourite books and Bayesian Data Analysis as another one… Or displaying Bayes [or his alleged portrait] and Turing in his book cover. So I went searching on the Web for more information about this surprising quote. And found the explanation, as given by Peter Norvig himself:

“To set the record straight: That’s a silly statement, I didn’t say it, and I disagree with it.”

Which means that weird quotes have a high probability of being misquotes. And used by others to (obviously) support their own agenda. In the current case, Chris Anderson and his End of Theory paradigm. Briefly and mildly discussed by Andrew a few years ago.

Bayes at the Bac’ [again]

Posted in Kids, Statistics with tags , , , , , , , , on June 19, 2014 by xi'an

When my son took the mathematics exam of the baccalauréat a few years ago, the probability problem was a straightforward application of Bayes’ theorem.  (Problem which was later cancelled due to a minor leak…) Surprise, surprise, Bayes is back this year for my daughter’s exam. Once again, the topic is a pharmaceutical lab with a test, test with different positive rates on two populations (healthy vs. sick), and the very basic question is to derive the probability that a person is sick given the test is positive. Then a (predictable) application of the CLT-based confidence interval on a binomial proportion. And the derivation of a normal confidence interval, once again compounded by  a CLT-based confidence interval on a binomial proportion… Fairly straightforward with no combinatoric difficulty.

The other problems were on (a) a sequence defined by the integral

\int_0^1 (x+e^{-nx})\text{d}x

(b) solving the equation

z^4+4z^2+16=0

in the complex plane and (c) Cartesian 2-D and 3-D geometry, again avoiding abstruse geometric questions… A rather conventional exam from my biased perspective.

Big Bayes stories in print [and in force]

Posted in Books, Statistics, University life with tags , , , , , on May 20, 2014 by xi'an

The special issue of Statistical Science Kerrie Mengersen and I edited over the past three (four?) years is now out in print! Even though many ‘Og readers may have already seen the table of contents, here it is once again. We hope you will enjoy this 100 page long excursion in big Bayesiana. The papers are not freely accessible as “current papers” on the journal website but can yet be found in the “future papers” section. (If a sponsor wants to support turning the papers into open access version, he or she is most welcome to contact us or the IMS!) And, thanks to Larry for reminding me!, available on arXiv. Thanks to all authors, discussants, reviewers and special kudos to Jon Wellner for his constant help and support in putting the special issue together!

Dennis Lindley (1923-2013)

Posted in Books, Statistics, University life with tags , , , , , , on December 16, 2013 by xi'an

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 thomasbayes@gmail.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!

Philosophy of Science, a very short introduction (and review)

Posted in Books, Kids, Statistics, Travel with tags , , , , , , , , , , , on November 3, 2013 by xi'an

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

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