Archive for subjectivity

RSS Read Paper

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , on April 17, 2017 by xi'an

I had not attended a Read Paper session at the Royal Statistical Society in Errol Street for quite a while and hence it was quite a treat to be back there, especially as a seconder of the vote of thanks for the paper of Andrew Gelman and Christian Hennig. (I realised at this occasion that I had always been invited as a seconder, who in the tradition of the Read Papers is expected to be more critical of the paper. When I mentioned that to a friend, he replied they knew me well!) Listening to Andrew (with no slide) and Christian made me think further about the foundations of statistics and the reasons why we proceed as we do. In particular about the meaning and usages of a statistical model. Which is only useful (in the all models are wrong meme) if the purpose of the statistical analysis is completely defined. Searching for the truth does not sound good enough. And this brings us back full circle to decision theory in my opinion, which should be part of the whole picture and the virtues of openness, transparency and communication.

During his talk, Christian mentioned outliers as a delicate issue in modelling and I found this was a great example of a notion with no objective meaning, in that it is only defined in terms of or against a model, in that it addresses the case of observations not fitting a model instead of a model not fitting some observations, hence as much a case of incomplete (lazy?) modelling as an issue of difficult inference. And a discussant (whose Flemish name I alas do not remember) came with the slide below of an etymological reminder that originally (as in Aristotle) the meaning of objectivity and subjectivity were inverted, in that the later meant about the intrinsic nature of the object, while the former was about the perception of this object. It is only in the modern (?) era that Immanuel Kant reverted the meanings…Last thing, I plan to arXiv my discussions, so feel free to send me yours to add to the arXiv document. And make sure to spread the word about this discussion paper to all O-Bayesians as they should feel concerned about this debate!

beyond objectivity, subjectivity, and other ‘bjectivities

Posted in Statistics with tags , , , , , , , , , , , , , on April 12, 2017 by xi'an

Here is my discussion of Gelman and Hennig at the Royal Statistical Society, which I am about to deliver!

objective and subjective RSS Read Paper next week

Posted in Books, pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , 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.

another Le Monde column

Posted in Books, Statistics, University life with tags , , , , , , , on February 16, 2012 by xi'an

Another column in Le Monde (Sciences) had most unjustly escaped my attention: it mentioned Thomas Bayes on the very front page and I missed it till my most recent breakfast! This article was written by a neuroscientist columnist reporting on current research led by Tali Sharot, UCL, on the prediction mechanisms (if not on her book). The argument is not only that the brain operates in a Bayesian fashion, actualising predictions based on current observations (as exposed at Bayes 250), but also that the updating is not “objective”! While this may sound as if the neuroscientists have entered the debate between objective and subjective Bayesians, the study actually reports a bias toward optimism, when comparing predictions with “objective statistics”. The article concludes on the psychological advantages of this optimism bias. Not so much about Bayesian statistics, then, even though having almost everyone (subconsciously) working with his/her optimistic prior sounds rather cool!

principles of uncertainty

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , on October 14, 2011 by xi'an

Bayes Theorem is a simple consequence of the axioms of probability, and is therefore accepted by all as valid. However, some who challenge the use of personal probability reject certain applications of Bayes Theorem.”  J. Kadane, p.44

Principles of uncertainty by Joseph (“Jay”) Kadane (Carnegie Mellon University, Pittsburgh) is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. Jay Kadane wrote Principles of uncertainty over a period of several years and, more or less in his own words, it represents the legacy he wants to leave for the future. The book starts with a large section on Jay’s definition of a probability model, with rigorous mathematical derivations all the way to Lebesgue measure (or more exactly the McShane-Stieltjes measure). This section contains many side derivations that pertain to mathematical analysis, in order to explain the subtleties of infinite countable and uncountable sets, and the distinction between finitely additive and countably additive (probability) measures. Unsurprisingly, the role of utility is emphasized in this book that keeps stressing the personalistic entry to Bayesian statistics. Principles of uncertainty also contains a formal development on the validity of Markov chain Monte Carlo methods that is superb and missing in most equivalent textbooks. Overall, the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. Continue reading

JSM [5]

Posted in pictures, Statistics, Travel, University life with tags , , , , on August 3, 2011 by xi'an

Another early day at JSM 2011, with a series of appointments at the Loews Hotel, whose only public outcome is that the vignettes on Bayesian statistics I called for in a previous post could end up being published in Statistical Science… I still managed to go back to the conference centre (almost) in time for Chris Holmes’ talk. Although I am sure Julien will be much more detailed about this Medallion Lecture talk, let me say that this was a very enjoyable and informative talk about the research Chris has brilliantly conducted so far! I like very much the emphasis on decision-theory, subjective Bayesianism, and hidden Markov models, while the application section was definitely impressive in the scope of the problems handled and the rich outcome of Chris’ statistical analyses, especially in connection with cancer issues…

In the afternoon I attended a Bayesian non-parametric session, before joining many others for the COPSS Awards session, where the awards were given to

  • COPSS:, Nilanjan Chatterjee, National Cancer Institute,
  • F.N. Dawid: Marie Davidian, North Carolina State University,
  • G.W. Snedecor: Nilanjan Chatterjee, National Cancer Institute,
  • R.A. Fisher Lecture: Jeff Wu, Georgia Tech. University,

seeing the same person being awarded two rewards twice for the first time.

The Search for Certainty

Posted in Books, Statistics with tags , , , , , , , , on January 25, 2010 by xi'an

“The expected value is hardly ever expected.” The Search for Certainty, page 207.

Following the advice of an Og’s reader, Erkan, I read Krzysztof Burdzy’s The Search for Certainty over the past weeks (and mostly in the métro). The author is primarily a probabilist, but he has set upon launching a radical criticism of the philosophical foundations of Statistics, the book subtitle being (somehow misleadingly) put as On the Clash of Science and Philosophy of Probability. Or so he thinks. (The introduction to the book is available on the author’s webpage and he has also started a blog related with the book. The cover is made of seven dices all showing sixes, with on top the probability p=0.0000036… of such an event, provided the dice is fair. And provided one does not take into account the suspicious fives all facing the reader!)

“Of the four well crystallized philosophies of probability, two chose the certainty as their intellectual holy grail. Those are the failed theories of von Mises and de Finetti.” The Search for Certainty, page 30.

Although I have read the book with a pen, I will not go at this stage into a detailed analysis of The Search for Certainty. Indeed, I found the book both annoying and unconvincing, for reasons not very different from the criticisms addressed at Taleb’s The Black Swan. The book aims at demonstrating that the philosophical arguments underlying both frequentist and Bayesian Statistics are wrong. Unsurprisingly (!), I find the book lacking in this demonstration and overall poor from a scholarly perspective. It compares with Taleb’s The Black Swan in that the attempts at philosophy are more related to everyday “common sense” than to deep (and scholarly) philosophy (and they also involve the apparently inevitable Karl Popper, “the champion of the propensity theory of probability”, p.43!). The main point made in The Search for Certainty is very narrow in that Burdzy concentrates on two very specific entries to frequentism and subjectivism, namely von Mises’ and de Finetti’s, respectively, while those are not your average statistician’s references. For instance, von Mises bases his definition of frequency properties on the notion of collectives, a notion I had not previously encountered. Similarly, de Finetti’s statement “Probability does not exist” cannot be seen as the core principle of many Bayesian statisticians and I certainly do not relate to his all-subjective perspective for conducting Bayesian inference.

“Mr. Winston is unique because we know something about him that we do not know about any other individual in the population.” The Search for Certainty, page 66.

The style of The Search for Certainty is fairly annoying, if of a different sort than Taleb‘s. It is predominantly non-technical, the worked-out examples being always of the coin and balls-in-an-urn type. Arguments are never more than one paragraph long and metaphors and weak analogies are more confusing than helpful. The book criticises a lot decision-theory and the related coherence of Bayesian procedures, ie against the Dutch Book argument, but it misses the connections between frequentist optimality(ies) and Bayesian procedures, like Wald’s complete class theorem, Welch and Peers (1964) matching priors, or the more recent Berger’s frequentist-Bayesian perspective. There are also (in my opinion) confusions, as when the basis for the frequency approach to probability is criticised for being connected with an unrealistic infinity of events, thus confusing concepts with experiments (indeed, the Large Law of Large Numbers cannot be proved by an experiment), the existence of a model versus its assessment (“Kolmogorov’s axioms say nothing on how to match the mathematical results with reality”, p.31), the use of a probability against its “truth”, the inclusion of time (and thus model shifts) into mathematical axioms, the assimilation of frequentist statistics to unbiased estimators, a somehow diffuse belief that some priors can be proven to be better than others, an argument that  they can be evaluated by their predictive performances… The insistence in adding new axioms to Kolmogorov’s is furthermore puzzling:

(L4) If there exists a symmetry on the space of possible outcomes which maps an event A onto an event B then the two events have equal probabilities, that is, P(A) = P(B).
(L5) An event has probability 0 if and only if it cannot occur. An event has probability 1 if and only if it must occur.

The axiom (L4) relates to both the Principle of Insufficient Reasons, whose limitations are the cause for much debate in the selection of prior distributions, and to invariance principles that lead to Haar measures as default noninformative priors. But I do not see the point in adding such an axiom into the tenets of probability. (And (L5) is more psychological than mathematical…)

“There is no justification for the use of the Bayes theorem in the subjective theory.” The Search for Certainty, page 144.

In conclusion, it is hopefully obvious that I did not overly enjoy this The Search for Certainty and that I do not consider it makes a significant contribution to the foundations of statistical inference and in particular to Bayesian analysis. Being examined by an outsider to our discipline certainly has a strong appeal, but only if done at a deep enough level.

Ps-Be warned that there is a homonymous book with full titlde The Search for Certainty: A Philosophical Account of Foundations of Mathematics on issues related with Gödel’s incompleteness theorem, by Marcus Gianquinto, book that I mistakenly bought for The Search for Certainty discussed here. Professor Gianquinto is actually a professor of philosophy at UCL, who specialises in epistemology so he could also comment on this book.