Archive for Significance
the true cost of war [cover]
Posted in Books, Kids, pictures, Statistics with tags Afghanistan, American Statistical Association, armed conflict, ASA, forced displacement, Gaza, International Rescue Committee, Islamic State, mobile phone metadata, Oxford University Press, Royal Statistical Society, RSS, Significance, taliban, Uppsala Conflict Data Program, war crimes, war in Gaza on April 9, 2025 by xi'an
the polls weren’t wrong [alt book review]
Posted in Statistics with tags applied mathematics, April fool, book review, CHANCE, Chapman & Hall, conspiracy theories, CRC Press, Donald Trump, FiveThirtyEight, political polls, polls, Significance, statistical literacy, US elections 2016, US elections 2020, US elections 2024 on April 1, 2025 by xi'an
Philosophies, Puzzles and Paradoxes [book review]
Posted in Books, pictures, Statistics, Travel, University life with tags A Treatise on Probability, Bayesian inference, Bill Reid, book review, British Columbia, Canada, cedar, CHANCE, David Hume, Enlightenment, epistemic probability, First Nations, frequentist confidence, Haida culture, Henri Poincaré, incompleteness theorem, jatp, John Maynard Keynes, Kurt Gödel, likelihood, Likelihood Principle, marginalisation paradoxes, Maurice Allais, Monty Hall problem, Museum of Anthropology, paradoxes, Philosophy of Science, prior selection, puzzle, raven, Significance, Tintin, UBC, University of British Columbia, Vancouver on May 25, 2024 by xi'an
Yudi Pawitan and Youngjo Lee have written a book that recently caught my attention within the CRC Press list of new publications. Because philosophy, puzzles, and paradoxes are definitely of interest to me (as shown by numerous entries in the ‘Og!). The subtitle of said book is A Statistician’s Search for Truth.
Reviews of the book are already available, with for instance Andrew Gelman stating that he disagrees “with much of this book, but it’s an entertaining and thought-provoking introduction to some challenging questions” or Stephen Senn starting the foreword with “This is a remarkable book: wide-ranging, ambitious, challenging and profound but also intriguing, fascinating and original.” (Senn is also cited within the book for his discussion of our revisit of Harold Jeffreys’ Theory of Probability.) Nice cover as well (albeit I could not trace the origin of it, inside or outside the book.)
The book is made of three parts, one on the philosophical approaches to truth, scientific discovery, deduction, and induction, a second one on probability theories, with philosophical motivations, Bayesian inference, and likelihood-based inference, and a third section on paradoxes. Given that both authors are senior authors who have contributed to likelihood inference throughout their career, incl. the books In All Likelihood and Generalized Linear Models with Random Effects, the likelihood approach is somewhat privileged against other statistical resolutions towards the resolution of the paradoxes, with a defence of confidence distributions and a chapter on epistemic confidence that mostly stems from recent papers by the authors, like Pawitan et al. (2023) and Lee and Lee (2023). I find the discussion therein somewhat unclear, esp. because the same notation Pr(.) is employed for different probability notions.
“Epistemic confidence is the objective measure of uncertainty that’s attached to single events, where the objectivity is based on a consensus of rational minds.” (p.197)
The philosophy part is following the (European) Enlightenment in producing more and more involved discussions on reason, knowledge and scientific discovery. This exploration is an easy read, as it does not delve particularly deeply in the arguments of Kant, Hume, or Popper. With the apparently unescapable mention of Gödel’s incompleteness theorem, including a sausage citation from Poincaré that reminded of that strip from Tintin in America:
which, most probably, he would have applied to Ais! Several sections about pseudo-rational attempts to demonstrate the existence of Dog could have been skipped as well.
The part of probability already considers paradoxes which, like the subsequent ones are mostly the consequence of using natural (and hence ambiguous) languages instead of mathematical descriptions—incl. the statement of the Likelihood Principle. It also discusses Keynes’ logical (or imprecise) probabilities, briefly if appropriately given the pessimistic views of young Keynes on the assessment of the probability of an event. Savage is privileged enough to enjoy an entire chapter discussing his 1950’s axioms leading to the existence of a (subjective) prior on “the states of the world”. This is followed by a chapter on Inverse probability (aka Bayesian statistics), where the authors consider Bayes’ 1763 Essay to have stayed mostly unnoticed till the beginning of the 20th Century, which sounds a somewhat subjective judgement. (And as uncovered by Steve Stiegler, the original title of the Essay was indeed intended as a reply to Hume.) A further if short chapter is dedicated to the search for the prior distribution. Which thus gives the misguided impression that there should exist such a thing, rather than acknowledging that Bayesian statements are relative to the prior measure. The remainder of the discussion on invariant and reference priors is however mostly standard. Except when falling for the marginalisation paradox when stating that a product of improper priors implies independence on p.144.
The paradoxes examined in the final part are Allais’ (an alumni of Lycée Lakanal!), and Ellsberg’s, avatars of the Saint Petersburg paradox and referring to failing to adhere to rational decision-making and not in the least to statistics. Conjunction and inclusion “fallacious fallacies”, which are central to Kahneman’s Thinking fast and slow bestseller, and attributed to reasoning in terms of likelihood rather than of probability (without accounting for multiple testing on p.228). A whole if short chapter on the Monty Hall and three prisoners paradoxes, another predictable occurrence in a book on reasoning paradoxes. Again mostly a matter of poor wording, plus relying on the choice of an underlying probability model, for which the authors again follow a likelihood approach, the number of the prize door or of the freed prisoner being the parameter. Kyburg’s (very weak) lottery paradox and related forensic paradoxes, concluding with the rejection of judgements based solely on probability reasoning. Hempel’s paradox of the ravens, a priori unrelated with statistical evidence, but turned into one by squeezing in some sampling models. Finishing with the (envelope) exchange paradox, where the authors refuse to put a prior on the unknown parameter but end up with a solution equivalent to adopting a Jeffreys prior.
In conclusion, this attempt at connecting statistical inference and philosophy, probability concepts and rational decision making, paradoxes and modelling, within a single book is academically sound and overall enjoyable, if not outstanding or remarkable as it does not constitute a radical move away from existing analyses of those classical paradoxes. Furthermore, I find the paradoxes overwhelmingly distant from genuine statistical settings and involving a rather stretched notion of data. Still, methinks I will keep this book in my bookcase, rather than leaving it for the taking in the department coffee room!
As I was completing the book and getting towards writing this book review, I also noticed a two page blurb in Significance (May 2024 issue) written by the authors on their book. (which happens rather frequently with this magazine). Unsurprisingly, the contents provd mostly extracted from the preface and introduction With a nice ravens picture (in conjunction with the raven paradox).
[Disclaimer about potential self-plagiarism: this post or an edited version may eventually appear in my Books Review section in CHANCE.]
Calyampudi Radhakrishna Rao (1920-2023)
Posted in Books, pictures, Statistics, University life with tags C.R. Rao, Calyampudi Radhakrishna Rao, handbook, India, Kolkata, Pitman nearness, Purdue University, R.A. Fisher, Rao-Blackwellisation, Significance, University of Calcutta, University of Cambridge on August 26, 2023 by xi'an
Just heard that C.R. Rao had passed away on Wednesday. Above is a 1941 picture I photographed while attending the jubilee of the Department of Statistics of the University of Calcuta. Showing R.A. Fisher and P.C. Mahalanobis surrounded by faculty and students from the Department. Including a very young Rao who would a few years later go to Cambridge and write a PhD thesis on ANOVA under the supervision of R.A. Fisher. While my own interactions with C.R. Rao have been quite limited, from attending a seminar dinner with him when he visited Purdue University in 1988, to writing a critical assessment of Pitman nearness that he reportedly disliked, to writing chapters in some of the handbooks he edited and a review paper on Rao-Blackwellisation for the International Statistical Review special issue for his 100th birthday (which almost coincided with mine, one day off), he stood as a giant of the field, having impacted statistics and beyond in many and profound ways. The Hindu published an obituary immediately after his death, while Current Science has a longer if older biography full of pictures and Significance a series of articles on “C.R. Rao’s Century”. However, I’d like to recall this quote of his’, acknowledging his mother for his work habits.
‘For instilling in me the quest for knowledge, I owe to my mother, A. Laxmikanthamma, who, in my younger days, woke me up every day at four in the morning and lit the oil lamp for me to study in the quiet hours of the morning when the mind is fresh.’
an hypothetical chain of transmissions
Posted in Books, Statistics, University life with tags Abbé Morellet, Condorcet, history of statistics, Pierre Simon Laplace, Richard Price, Significance, Thomas Bayes on August 6, 2021 by xi'an
