**A** few months ago, Andrew Gelman collated and commented the reviews of Deborah Mayo’s book by himself, Brian Haig, Christian Hennig, Art B. Owen, Robert Cousins, Stan Young, Corey Yanofsky, E.J. Wagenmakers, Ron Kenett, Daniel Lakeland, and myself. The collection did not make it through the review process of the Harvard Data Science Review! it is however available on-line for perusal…

## Archive for Deborah Mayo

## perspectives on Deborah Mayo’s Statistics Wars

Posted in Statistics with tags Andrew Gelman, book review, Deborah Mayo, Statistical Inference as Severe Testing, statistics wars on October 23, 2019 by xi'an## Bertrand-Borel debate

Posted in Books, Statistics with tags Bayes factor, Bayesian hypothesis testing, Bayesian model selection, Bertrand's paradox, conditioning, Deborah Mayo, Emile Borel, Erich Lehmann, Joseph Bertrand, Le Hasard, Pierre Simon Laplace, Pleiades, posterior probability, uniformly most powerful tests on May 6, 2019 by xi'an**O**n her blog, Deborah Mayo briefly mentioned the Bertrand-Borel debate on the (in)feasibility of hypothesis testing, as reported [and translated] by Erich Lehmann. A first interesting feature is that both [starting with] B mathematicians discuss the probability of causes in the Bayesian spirit of Laplace. With Bertrand considering that the prior probabilities of the different causes are impossible to set and then moving all the way to dismiss the use of probability theory in this setting, nipping the p-values in the bud..! And Borel being rather vague about the solution probability theory has to provide. As stressed by Lehmann.

“The Pleiades appear closer to each other than one would naturally expect. This statement deserves thinking about; but when one wants to translate the phenomenon into numbers, the necessary ingredients are lacking. In order to make the vague idea of closeness more precise, should we look for the smallest circle that contains the group? the largest of the angular distances? the sum of squares of all the distances? the area of the spherical polygon of which some of the stars are the vertices and which contains the others in its interior? Each of these quantities is smaller for the group of the Pleiades than seems plausible. Which of them should provide the measure of implausibility? If three of the stars form an equilateral triangle, do we have to add this circumstance, which is certainly very unlikely apriori, to those that point to a cause?” Joseph Bertrand (p.166)

“But whatever objection one can raise from a logical point of view cannot prevent the preceding question from arising in many situations: the theory of probability cannot refuse to examine it and to give an answer; the precision of the response will naturally be limited by the lack of precision in the question; but to refuse to answer under the pretext that the answer cannot be absolutely precise, is to place oneself on purely abstract grounds and tomisunderstand the essential nature of the application of mathematics.” Emile Borel (Chapter 4)

Another highly interesting objection of Bertrand is somewhat linked with his conditioning paradox, namely that the density of the observed unlikely event depends on the choice of the statistic that is used to calibrate the unlikeliness, which makes complete sense in that the information contained in each of these statistics and the resulting probability or likelihood differ to an arbitrary extend, that there are few cases (monotone likelihood ratio) where the choice can be made, and that Bayes factors share the same drawback if they do not condition upon the entire sample. In which case there is no selection of “circonstances remarquables”. Or of uniformly most powerful tests.

## reading pile for X break

Posted in Books, pictures, Statistics, Travel, University life with tags AIQ, algorithms, beauty, book reviews, Cahiers du CNRS, CNRS, computer science, Deborah Mayo, England, mathematics, NIck Polson, reading list, Scotland, severe testing, University of Warwick on December 28, 2018 by xi'an## severe testing or severe sabotage? [not a book review]

Posted in Books, pictures, Statistics, University life with tags Cambridge University Press, commercial editor, cup, Deborah Mayo, philosophy of sciences, print on demand, severe testing, statistical inference, statistics wars, testing of hypotheses on October 16, 2018 by xi'an**L**ast week, I received this new book of Deborah Mayo, which I was looking forward reading and annotating!, but thrice alas, the book had been sabotaged: except for the preface and acknowledgements, the entire book is printed upside down [a minor issue since the entire book is concerned] and with some part of the text cut on each side [a few letters each time but enough to make reading a chore!]. I am thus waiting for a tested copy of the book to start reading it in earnest!

## “an outstanding paper that covers the Jeffreys-Lindley paradox”…

Posted in Statistics, University life with tags Aris Spanos, Bayesian model choice, Deborah Mayo, Error-Statistical philosophy, Harold Jeffreys, Jeffreys-Lindley paradox, Philosophy of Science, referee, severity on December 4, 2013 by xi'an

“This is, in this revised version, an outstanding paper that covers the Jeffreys-Lindley paradox (JLP) in exceptional depth and that unravels the philosophical differences between different schools of inference with the help of the JLP. From the analysis of this paradox, the author convincingly elaborates the principles of Bayesian and severity-based inferences, and engages in a thorough review of the latter’s account of the JLP in Spanos (2013).” Anonymous

**I** have now received a second round of reviews of my paper, “On the Jeffreys-Lindleys paradox” (submitted to Philosophy of Science) and the reports are quite positive (or even extremely positive as in the above quote!). The requests for changes are directed to clarify points, improve the background coverage, and simplify my heavy style (e.g., cutting Proustian sentences). These requests were easily addressed (hopefully to the satisfaction of the reviewers) and, thanks to the week in Warwick, I have already sent the paper back to the journal, with high hopes for acceptance. The new version has also been arXived. I must add that some parts of the reviews sounded much better than my original prose and I was almost tempted to include them in the final version. Take for instance

“As a result, the reader obtains not only a better insight into what is at stake in the JLP, going beyond the results of Spanos (2013) and Sprenger (2013), but also a much better understanding of the epistemic function and mechanics of statistical tests. This is a major achievement given the philosophical controversies that have haunted the topic for decades. Recent insights from Bayesian statistics are integrated into the article and make sure that it is mathematically up to date, but the technical and foundational aspects of the paper are well-balanced.” Anonymous

## Deborah Mayo’s talk in Montréal (JSM 2013)

Posted in Books, Statistics, Uncategorized with tags Allan Birnbaum, Deborah Mayo, JSM 2013, Likelihood Principle, Montréal, Sufficiency principle, weak conditionality principle on July 31, 2013 by xi'an**A**s posted on her blog, Deborah Mayo is giving a lecture at JSM 2013 in Montréal about why Birnbaum’s derivation of the Strong Likelihood Principle (SLP) is wrong. Or, more accurately, why *“WCP entails SLP”*. It would have been a great opportunity to hear Deborah presenting her case and I am sorry I am missing this opportunity. (Although not sorry to be in the beautiful Dolomites at that time.) Here are the slides:

**D**eborah’s argument is the same as previously: there is no reason for the inference in the mixed (or Birnbaumized) experiment to be equal to the inference in the conditional experiment. As previously, I do not get it: the weak conditionality principle (WCP) implies that inference from the mixture output, once we know which component is used (hence rejecting the* “and we don’t know which”* on slide 8), should only be dependent on that component. I also fail to understand why either WCP or the Birnbaum experiment refers to a mixture (sl.13) in that the index of the experiment is assumed to be known, contrary to mixtures. Thus (still referring at slide 13), the presentation of Birnbaum’s experiment is erroneous. It is indeed impossible to force the outcome of y* if tail and of x* if head *but* it is possible to choose the experiment index at random, 1 versus 2, and then, if y* is observed, to report (E_{1},x*) as a sufficient statistic. (Incidentally, there is a typo on slide 15, it should be “likewise for x*”.)