Archive for Purdue University

35 years ago…

Posted in Books, Kids, Statistics, Travel, University life with tags , , , , , , , , on July 2, 2022 by xi'an

What is luck? [book review]

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , on December 10, 2021 by xi'an

I was sent—by Columbia University Press—this book for a potential review in CHANCE: What are the chances? (Why we believe in luck?) was written by Barbara Blatchley, professor of Psychology and Neuroscience at Agnes Scott College in Decatur, Georgia. I have read rather quickly its 193 pages over the recent trips I made to Marseille and Warwick. The topic is truly about luck and the psychology of the feeling of being luck or unlucky. There is thus rather little to relate to as a statistician, as this is not a book about chance! (I always need to pay attention when using both words, since, in French chance primarily means luck, while malchance means bad luck. And the French term for chance and randomness is hasard…) The book is pleasant to read, even though the accumulation of reports about psychological studies may prove tiresome in the long run and, for a statistician, worrisome as to which percentage of such studies were properly validated by statistical arguments…

“…the famous quote by Louis Pasteur: “Dans les champs de l’observation, le hasard ne favorise que les esprits préparés”s (…) Pasteur never saw a challenge he couldn’t overcome with patience and preparation.” (p.19)

Even the part about randomness is a-statistical and mostly a-probabilist, rather focusing on our subjective and biased (un)ability to judge randomness. The author introduces us to the concepts of apophenia, which is “the unmotivated seeing of connections accompanied with a specific feeling of abnormal meaningfulness”, and of patternicity for the “tendency to find meaningful patterns in meaningless noise”. She also states that (Neyman-Pearson) Type I error is about seeing a pattern in random noise while Type II errors are for conclusion of meaningless when the data is meaningful (p.15). Which is reductive to say the least, but lead her to recall the four types of luck proposed by James Austin (which I first misread as Jane Austin).

“There is a long-standing and deeply intimate connection between luck, religion, and belief in the supernatural.” (p.28)

I enjoyed very much the sections on these connections between a belief in luck and religions, even though the anthropological references to ancient religions are not strongly connected to luck, but rather to the belief that gods and goddesses could modify one’s fate (and avoiding the most established religions). Still, I appreciate her stressing the fact that if one believes in luck (as opposed to sheer randomness), this expresses at the very least a form of irrational belief in higher powers that can bend randomness in one’s favour (or disfavour). Which is the seed for more elaborate if irrational beliefs. (For illustrations, Borgès’ stories come to mind.)

“B.F. Skinner believed that superstitious behaviour was a consequence of learning and reinforcement.” (p.85)

There are also parts where (a belief in) luck and (human) learning are connected, but, unfortunately, no mention is made of the (vaguely) Bayesian nature of the (plastic, p. 188) brain modus operandi. The large section on the brain found in the book is instead physiological, since concerned with finding regions where the belief in luck could be located. In relation with attention-deficit disorders. (Revealing the interesting existence (for me) of mirror neurons, dedicated to predicting what could happen! Described as “predictive coding”, p.153). The last chapter “How to get lucky” contains a rather lengthy account of “Clever Hans”, the 1990 German counting horse (!). Who, as well-known, reacted to subtle and possibly unconscious signals from his trainer rather than to an equine feeling for arithmetic…

One of the clearest conclusions of the book is (imho) that a belief in luck may improve the life of the believers, while a belief in being unlucky may deteriorate it. The Taoist tale finishing the book is a pure gem. But I am still in the dark as to whether or not my exceptional number of bike punctures in the past year qualifies as bad luck!

“Luck is the way you face the randomness of the world.” (p.191)

As an irrelevant aside, one anecdote at the beginning of the book brought back memories of the Wabash River flowing through Lafayette, IN, as it tells of the luck of two Purdue female rowers who attempted a transatlantic race and survived capsizing in the middle of the Atlantic. It also made me regret I had not realised at the time there was a rowing opportunity there!

three decades back

Posted in Kids, Travel with tags , , , , , , , , , on October 25, 2021 by xi'an

Yesterday, I (we) found myself (ourselves) back in time, precisely 34 years ago, as we drove our daughter to Orly airport for her flight to Cayenne, French Guiana. And the start of her internship. Indeed, this is also the airport from which I left for Purdue University in 1987 and where my parents drove me then, more for sentimental reasons than out of necessity, as I had much less luggage than Rachel! This old airport has not changed that much, apart from the sharp increase in security restrictions. At the time, my parents were able to stay till the plane to Chicago left (two hours late) and watch it take off from the terraces of the airport. This time, we were just unable to enter the airport beyond the parking lot and watched the plane take off (one hour late) from a flight tracker! But overall there was the same bittersweet feeling of seeing one’s kid move (far) away for a major and exciting step in their professional life. (When I called my mom to watch for the plane flying west straight across Normandy, very close to our family roots, she reminded me of that and also of my grand-parents watching my plane flying by… Without a flight tracker! I actually remember spotting Mont Saint-Michel on that trip.) Fare well, Dr. R, and see you soon!

estimation of a normal mean matrix

Posted in Statistics with tags , , , , , , , , , on May 13, 2021 by xi'an

A few days ago, I noticed the paper Estimation under matrix quadratic loss and matrix superharmonicity by Takeru Matsuda and my friend Bill Strawderman had appeared in Biometrika. (Disclaimer: I was not involved in handling the submission!) This is a “classical” shrinkage estimation problem in that covariance matrix estimators are compared under under a quadratic loss, using Charles Stein’s technique of unbiased estimation of the risk is derived. The authors show that the Efron–Morris estimator is minimax. They also introduce superharmonicity for matrix-variate functions towards showing that generalized Bayes estimator with respect to a matrix superharmonic priors are minimax., including a generalization of Stein’s prior. Superharmonicity that relates to (much) earlier results by Ed George (1986), Mary-Ellen Bock (1988),  Dominique Fourdrinier, Bill Strawderman, and Marty Wells (1998). (All of whom I worked with in the 1980’s and 1990’s! in Rouen, Purdue, and Cornell). This paper also made me realise Dominique, Bill, and Marty had published a Springer book on Shrinkage estimators a few years ago and that I had missed it..!

the buzz about nuzz

Posted in Books, Mountains, pictures, Statistics with tags , , , , , , , , , , , , , on April 6, 2020 by xi'an

“…expensive in these terms, as for each root, Λ(x(s),v) (at the cost of one epoch) has to be evaluated for each root finding iteration, for each node of the numerical integral

When using the ZigZag sampler, the main (?) difficulty is in producing velocity switch as the switches are produced as interarrival times of an inhomogeneous Poisson process. When the rate of this process cannot be integrated out in an analytical manner, the only generic approach I know is in using Poisson thinning, obtained by finding an integrable upper bound on this rate, generating from this new process and subsampling. Finding the bound is however far from straightforward and may anyway result in an inefficient sampler. This new paper by Simon Cotter, Thomas House and Filippo Pagani makes several proposals to simplify this simulation, Nuzz standing for numerical ZigZag. Even better (!), their approach is based on what they call the Sellke construction, with Tom Sellke being a probabilist and statistician at Purdue University (trivia: whom I met when spending a postdoctoral year there in 1987-1988) who also wrote a fundamental paper on the opposition between Bayes factors and p-values with Jim Berger.

“We chose as a measure of algorithm performance the largest Kolmogorov-Smirnov (KS) distance between the MCMC sample and true distribution amongst all the marginal distributions.”

The practical trick is rather straightforward in that it sums up as the exponentiation of the inverse cdf method, completed with a numerical resolution of the inversion. Based on the QAGS (Quadrature Adaptive Gauss-Kronrod Singularities) integration routine. In order to save time Kingman’s superposition trick only requires one inversion rather than d, the dimension of the variable of interest. This nuzzled version of ZIgZag can furthermore be interpreted as a PDMP per se. Except that it retains a numerical error, whose impact on convergence is analysed in the paper. In terms of Wasserstein distance between the invariant measures. The paper concludes with a numerical comparison between Nuzz and random walk Metropolis-Hastings, HMC, and manifold MALA, using the number of evaluations of the likelihood as a measure of time requirement. Tuning for Nuzz is described, but not for the competition. Rather dramatically the Nuzz algorithm performs worse than this competition when counting one epoch for each likelihood computation and better when counting one epoch for each integral inversion. Which amounts to perfect inversion, unsurprisingly. As a final remark, all models are more or less Normal, with very smooth level sets, maybe not an ideal range


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