which thus uses the Laplacian as a natural and normalisation-free penalisation for the score test. (Score that I first met in Padova, a few weeks before moving from X to IX.) Which brings a decision-theoretic alternative to the Bayes factor and which delivers a coherent answer when using improper priors. Thus a very appealing proposal in my (biased) opinion! The paper is mostly computational in that it proposes SMC and SMC² solutions to handle the estimation of the Hyvärinen score for models with tractable likelihoods and tractable completed likelihoods, respectively. (Reminding me that Pierre worked on SMC² algorithms quite early during his Ph.D. thesis.)

A most interesting remark in the paper is to recall that the Hyvärinen score associated with a generic model on a series must be the prequential (predictive) version

rather than the version on the joint marginal density of the whole series. (Followed by a remark within the remark that the logarithm scoring rule does not make for this distinction. And I had to write down the cascading representation

to convince myself that this unnatural decomposition, where the posterior on θ varies on each terms, is true!) For consistency reasons.

This prequential decomposition is however a plus in terms of computation when resorting to sequential Monte Carlo. Since each time step produces an evaluation of the associated marginal. In the case of state space models, another decomposition of the authors, based on measurement densities and partial conditional expectations of the latent states allows for another (SMC²) approximation. The paper also establishes that for non-nested models, the Hyvärinen score as a model selection tool asymptotically selects the closest model to the data generating process. For the divergence induced by the score. Even for state-space models, under some technical assumptions. From this asymptotic perspective, the paper exhibits an example where the Bayes factor and the Hyvärinen factor disagree, even asymptotically in the number of observations, about which mis-specified model to select. And last but not least the authors propose and assess a discrete alternative relying on finite differences instead of derivatives. Which remains a proper scoring rule.

I am quite excited by this work (call me biased!) and I hope it can induce following works as a viable alternative to Bayes factors, if only for being more robust to the [unspecified] impact of the prior tails. As in the above picture where some realisations of the SMC² output and of the sequential decision process see the wrong model being almost acceptable for quite a long while…

Filed under: pictures, Statistics, Travel Tagged: Bayes factor, Bayesian model comparison, Bayesian model selection, consistency, Harvard University, Hyvärinen score, Lévy diffusion process, logarithmic score, Padova, penalisation, prior predictive, sequential Monte Carlo, SMC, SMC² ]]>

Filed under: Statistics Tagged: Domaine de Montcalmès, French wines, Languedoc wines, Les Papilles, Montpellier, Paris, Pic Saint Loup, Puéchabon, Terrasses du Larzac ]]>

*“Exceptions might have to be made for experts such as statisticians and bioinformaticians whose skills are required on many papers.”*

**O**ne of these weird editorials periodically occurring in Nature. By Brian Martinson, suggesting that the number of words allotted to a scientist should be capped. Weird, indeed, and incomprehensible that Nature wastes one of its so desperately sought journal page on such a fantastic (in the sense of fantasy, not as in great!) proposal. With sentences like “if we don’t address our own cognitive biases and penchant for compelling narratives, word limits could exacerbate tendencies to publish only positive findings, leading researchers to explore blind alleys that others’ negative results could have illuminated” not making much sense even in this fantasy academic world… As for the real world, the list of impossibilities and contradictions stemming from this proposal would certainly eat all of my allotted words. Even those allotted to a statistician. The supreme irony of the (presumably tongue-in-cheek) editorial is that the author himself does not seem particularly concerned by capping his own number of papers! (Nice cover, by the way!)

Filed under: Books, Kids, pictures, University life Tagged: editorial, Nature, predatory publishing, publication ]]>

*“How does it do this? Pears, not traditionally a science fiction writer, employs some commonly used devices of the genre to create a mind-bending but wholly satisfying tale…”* Robin’s Books

*“Indeed, Arcadia seems to be aimed at the lucrative crossover point between the grownup and YA markets, even if it lacks the antic density of the Harry Potter series or the focused peril of The Hunger Games.” Steven Poole, The Guardian
*

**T**he picture above is completely unrelated with the book if not the title. (And be at rest: I am not going to start an otter theme in the spirit of Andrew’s cats… Actually a cat plays a significant role in this book.) But Pears’ Arcadia is a fairly boring tale and an attempt at a rather dry play on the over-exploited theme of time-travel. Yaaawny, indeed!

I am fairly disappointed by this book, the more because Pears’ An Instance at the Fingerpost is a superb book, one of my favourites!, with a complexity of threads and levels, while maintaining a coherence of the plot that makes the final revelation a masterpiece. The Dream of Scipio also covers several historical periods of French Provence with a satisfactory plot and deep enough background (fed by a deep knowledge of the area and the eras…). The background, the broader perspective, the deep humanity of the characters, all these qualities of Pears’ books are lost in Arcadia, which sums up as an accumulation of clichés on dystopias, time-travel, and late 1950’s Oxford academics. *[Warning, spoilers ahoy!]* The parallel (and broadly medieval) universe to which the 20th century characters time-travel has some justifications for being a new type of Flatland: it is the creation of a single Oxonian academic, a mix of J.R. Tolkien and Eric Ambler. But these 20th century characters are equally charicaturesque. And so are the oppressors and the rebels in the distant future. (Set on the Isle of Mull, of all places!) And the mathematics of the time-travel apparatus are carefully kept hidden (with the vague psychomathematics there reminding me of the carefully constructed Asimov’s psychohistory.)

There is a point after which pastiches get stale and unattractive. And boring, so Yawn again. (That the book came to be shortlisted for the Arthur C. Clarke award this year is a mystery.)

Filed under: Books, pictures, Travel Tagged: An instance of the fingerpost, Arcadia, Arthur C. Clarke, fantasy, Foundation, Iain Peers, Isaac Asimov, Isle of Mull, otter, Oxford, science fiction, time travel, Tolkien, yawn ]]>

Filed under: Kids, pictures Tagged: AC/DC, Australia, Highway to Hell, It's a long way to the top, Malcom Young, Melbourne, rock'n roll ]]>

Filed under: Statistics Tagged: American Psychological Association, APA, APA style, BibTeX, LaTeX, paper, WIREs ]]>

Finding that once most causes for discrepancies (like gentle versus rough lab technicians!) were eliminated, there were still two “types” of worms, those short-lived and those long-lived, for reasons yet unclear. “We need to repeat more experiments than we realized” is a welcome conclusion to this dedicated endeavour, worth repeating in different circles. And apparently missing in the NYT coverage by Susan Dominus of the story of Amy Cuddy, a psychologist at the origin of the “power pose” theory that got later disputed for lack of reproducibility. Article which main ideological theme is that Cuddy got singled-out in the replication crisis because she is a woman and because her “power pose” theory is towards empowering women and minorities. Rather than because she keeps delivering the same message, mostly outside academia, despite the lack of evidence and statistical backup. (Dominus’ criticisms of psychologists with “an unusual interest in statistics” and of Andrew’s repeated comments on the methodological flaws of the 2010 paper that started all are thus particularly unfair. A Slate article published after the NYT coverage presents an alternative analysis of this affair. Andrew also posted on Dominus paper, with a subsequent humongous trail of comments!)

Filed under: Books, pictures, Statistics, University life Tagged: ageing, Amy Cuddy, Nature, NYT, power pose, psychology, replication crisis, roundworms, Slate, The New York Times ]]>

While n! cannot be a squared integer for n>1, does there exist 1<n<28 such that 28(n!) is a square integer? Does there exist 1<n,m<28 such that 28(n!)(m!) is a square integer? And what is the largest group of distinct integers between 2 and 27 such that the product of 28! by their factorials is a square?

**T**he fact that n! cannot be a square follows from the occurrence of single prime numbers in the resulting prime number decomposition. When considering 28!, there are several single prime numbers like 17, 19, and 23, which means n is at least 23, but then the last prime in the decomposition of 28! being 7 means this prime remains alone in a product by any n! when n<28. However, to keep up with the R resolution tradition, I started by representing all integers between 2 and 28 in terms of their prime decomposition:

primz=c(2,3,5,7,11,13,17,19,23) dcmpz=matrix(0,28,9) for (i in 2:28){ for (j in 1:9){ k=i while (k%%primz[j]==0){ k=k%/%primz[j];dcmpz[i,j]=dcmpz[i,j]+1}} }

since the prime number factorisation of the factorials n! follows by cumulated sums (over the rows) of dcmpz, after which checking for one term products

fctorz=apply(dcmpz,2,cumsum) for (i in 23:28) if (max((fctorz[28,]+fctorz[i,])%%2)==0) print(i)

and two term products

for (i in 2:28) for (j in i:27) if (max((fctorz[28,]+fctorz[i,]+fctorz[j,])%%2)==0) print(c(i,j))

is easy and produces i=28 [no solution!] in the first case and (i,j)=(10,27) in the second case. For the final question, adding up to twelve terms together still produced solutions so I opted for the opposite end by removing one term at a time and

for (a in 2:28) if (max(apply(fctorz[-a,],2,sum)%%2)==0) print(a)

exhibited a solution for a=14. Meaning that

2! 3! …. 13! 15! …. 28!

is a square.

Filed under: Books, Kids Tagged: factorial, Le Monde, mathematical puzzle, prime numbers ]]>

Filed under: Books, Statistics Tagged: cross validated, Don Fraser, exponential families, George Darmois, mathematical statistics, Pitman-Koopman theorem, proof, Stanford University, sufficient statistics ]]>

“I take issue with your assumption that advice on the Metropolis Algorithm is useless to me because of my ignorance of variates. I am currently taking an experimental course on Bayesian data inference and I’m enjoying it very much, i believe i have a relatively good understanding of the algorithm, but i was unclear about this specific.”

despite pondering the meaning of the call to rnorm(1)… I will keep this question in store to use in class when I teach Metropolis-Hastings in a couple of weeks.

Filed under: Books, Kids, R, Statistics, University life Tagged: cross validated, Gaussian random walk, Markov chain Monte Carlo algorithm, MCMC, Metropolis-Hastings algorithm, Monte Carlo Statistical Methods, normal distribution, normal generator, random variates ]]>