The Guardian published earlier this week a general public review of David Spiegelhalter’s most recent book, The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk, and Luck, about to be published by W. W. Norton & Company (according to Amazon). A review written by John Naughton, staying rather general (with the main examples selected for the review being the birthday problem, and the typing monkey not doing great after 1300 days hitting one key per second at random) and constantly positive, which is not surprising given David’s talents at telling tales about our trade! (And with deeper comments by David Hand and Adrian Smith.) Coïncidence or correlation? David also had a new entry in his philosophy column the very same week, about luck (in plane accidents and in the sequence of lucky events that led to his being born). The cover refers to double yolkers, a great example of apparent luck that David has used many times as not so random! (Warning: there are several books sharing the same title!)
Archive for egg double yolks
The Art of Uncertainty [not my book review]
Posted in Books, Statistics with tags book review, cover, David Spiegelhalter, egg double yolks, luck, Philosophy of Science, professor of risk, The Guardian, uncertainty on October 26, 2024 by xi'anpure birth process
Posted in Statistics with tags birth process, differential equation, Easter, egg double yolks, Geometric distribution, The Riddler, Yule on April 18, 2020 by xi'an
The Riddler has a rather simplistic riddle this week since it essentially asked for the expectation of a pure birth process (also known as the Yule process) at time t. Since the population size at time t has a geometric distribution with expectation
eλt.
It however took me a while to recover this result on my own on Easter afternoon, as I went for the integrals rather than the distribution itself and the associated differential equations. Interestingly (in a local sense!), I first following the wrong path of looking at the average time to the first birth, 1/λ, then to the second, 2/λ, and so on. Wrong since of course expectations do not carry this way… For a unit rate, λ=1, the average time to reach 10 births is about 3, while the average number of births over t=3 is essentially 20.
double yolk priors [a reply from the authors]
Posted in Books, Statistics, University life with tags Brad Efron, David Spiegelhalter, egg double yolks, empirical Bayes methods, frequentist inference, reply on March 14, 2018 by xi'an
, in eq (2.2), as it lives in the Hilbert space L2(G)double yolk priors
Posted in Statistics with tags Brad Efron, David Spiegelhalter, egg double yolks, empirical Bayes methods, frequentist inference on March 13, 2018 by xi'an
“To develop a “defendable and defensible” Bayesian learning model, we have to go beyond blindly ‘turning the crank’ based on a “go-as-you-like” [approximate guess] prior. A lackluster attitude towards prior modeling could lead to disastrous inference, impacting various fields from clinical drug development to presidential election forecasts. The real questions are: How can we uncover the blind spots of the conventional wisdom-based prior? How can we develop the science of prior model-building that combines both data and science [DS-prior] in a testable manner – a double-yolk Bayesian egg?”
I came through R bloggers on this presentation of a paper by Subhadeep Mukhopadhyay and Douglas Fletcher, Bayesian modelling via goodness of fit, that aims at solving all existing problems with classical Bayesian solutions, apparently! (With also apparently no awareness of David Spiegelhalter’s take on the matter.) As illustrated by both quotes, above and below:
“The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a Bayes-frequentist consolidated data analysis work ow that is more effective than either of the two separately.”
(I wonder who else in this Universe would characterise “modern Bayesian statistics” in such a non-Bayesian way! And love the notion of distillation applied to priors!) The setup is actually one of empirical Bayes inference where repeated values of the parameter θ drawn from the prior are behind independent observations. Which is not the usual framework for a statistical analysis, where a single value of the parameter is supposed to hide behind the data, but most convenient for frequency based arguments behind empirical Bayes methods (which is the case here). The paper adopts a far-from-modern discourse on the “truth” of “the” prior… (Which is always conjugate in that Universe!) Instead of recognising the relativity of a statistical analysis based on a given prior.
When I tried to read the paper any further, I hit a wall as I could not understand the principle described therein. And how it “consolidates Bayes and frequentist, parametric and nonparametric, subjective and objective, quantile and information-theoretic philosophies.”. Presumably the lack of oxygen at the altitude of Chamonix…. Given an “initial guess” at the prior, g, a conjugate prior (in dimension one with an invertible cdf), a family of priors is created in what first looks like a form of non-parametric exponential tilting of g. But a closer look [at (2.1)] exposes the “family” as the tautological π(θ)=g(θ)x π(θ)/g(θ). The ratio is expanded into a Legendre polynomial series. Which use in Bayesian statistics dates a wee bit further back than indicated in the paper (see, e.g., Friedman, 1985; Diaconis, 1986). With the side issue that the resulting approximation does not integrate to one. Another side issue is that the coefficients of the Legendre truncated series are approximated by simulations from the prior [Step 3 of the Type II algorithm], rarely an efficient approach to the posterior.
double-yolkers
Posted in Kids, Statistics with tags Brittany, chocolate mousse, coincidence, David Spiegelhalter, egg double yolks, eggs, galettes, yolk on November 14, 2013 by xi'an
Last night I was cooking buckwheat pancakes (galettes de sarrasin) from Brittany with an egg-and-ham filling. The first egg I used contained a double yolk, a fairly rare occurrence, at least in my kitchen! Then came the second pancake and, unbelievably!, a second egg with a double yolk! This sounded too unbelievable to be…unbelievable! The experiment stopped there as no one else wanted another galette, but tonight, when making chocolate mousse, I 
checked whether or not the four remaining eggs also were double-yolkers…and indeed they were. Which does not help when separating yolks from white, by the way. Esp. with IX fingers. At some stage, during the day, I remembered a talk by Prof of Risk David Spiegelhalter mentioning the issue, even including a picture of an egg-box with the double-yolker guarantee, as in the attached picture. But all I could find first was this explanation on BBC News. Which made sense for my eggs, as those were from a large calibre egg-box (which I usually do not buy)… (And then I typed David Spiegelhalter plus ‘double-yolker” on Google and all those references came out!)
