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.]
Read (over the past months) books I forgot to record in the Journal series namely, The Practice, the Horizon, and the Chain, by Sofia Samatar, a rather terrible take on Wells’ Time Machine where exploited live in the darkest parts of a space-ship and upper classes in the nicest places. With an unconvincing trio of characters and a paper-thin scenario, including an unconvincing pastiche of academic pettiness. Quite the disappointment! The latest Ben Aaronovitch’s Rivers of London novel, Stone & Sky, a rather nice instalment in the series, if only because it is set in Northern Scotland (where I read it!), but with some weaknesses in the plot and a puzzling two-voice narrative that sounds unbalanced (in favour of Peter vs. Abigail). Plus a wee bit caricaturing Scottish people, methinks! And then, being a Hugo voting member for 2026, several books and short stories that I receive as part of the LACon package, like The Raven Scholar by Antonia Hodgson read first because I love ravens! Especially the fantastic Ka: Dar Oakley in the Ruin of Ymr. I had trouble beginning the book, but once the setting was established, I could follow the main character more easily. The character is enticing but the universe building is shaky and the scenario weak on many planes, making the central issues of solving a murder and finding a new emperor/ress more of a summer camp challenge than crucial problems. Plus an all-too-common fixation on meals and drinks consumed by the characters… It is getting worse towards the end. Likely my (first and) last volume in the Eternal Path Trilogy! Not high in my Hugo ranking then. And the (Murderbot) novelette “Rapport: Friendship, Solidarity, Communion, Empathy” by Martha Wells. Frankly disappointing. I do love the Murderbot series, but this short story highly disappointed me. Between feelings of déjà vu and annoyance at the constant bickering between the characters that reminded me of the nadir of the relationship between my two kids! Absolutely worth ignoring! Even in the Hugo ranking.
Due to repeated travel, plus a heat wave, I did not cook much besides salads and fruit purées, but enjoyed a haggis pie on Skye. And two (local versions of) pissaladières in Marseille. I also had to transfer my olives of the (2025) year into new jars as some had started to grow mould. Fortunately. most of them remained edible if somewhat sour. Thanks to Omiros’ expert advice, they are now maturing in olive oil.
