The Effect [book review]

While it sounds like the title of a science-fiction catastrophe novel or of a (of course) convoluted nouveau roman, this book by Nick Huntington-Klein is a massive initiation to econometrics and causality. As explained by the subtitle, An Introduction to Research Design and Causality.

This is a hüûüge book, actually made of two parts that could have been books (volumes?). And covering three langages, R, Stata, and Python, which should have led to three independent books. (Seriously, why print three versions when you need at best one?!)  I carried it with me during my vacations in Central Québec, but managed to loose my notes on the first part, which means missing the opportunity for biased quotes! It was mostly written during the COVID lockdown(s), which may explain for a certain amount of verbosity and rambling around.

“My mom loved the first part of the book and she is allergic to statistics.”

The first half (which is in fact a third!) is conceptual (and chatty) and almost formula free, based on the postulate that “it’s a pretty slim portion of students who understand a method because of an equation” (p.xxii). For this reader (or rather reviewer) and on explanations through example, it makes the reading much harder as spotting the main point gets harder (and requires reading most sentences!). And a very slow start since notations and mathematical notions have to be introduced with an excess of caution (as in the distinction between Latin and Greek symbols, p.36). Moving through single variable models, conditional distributions, with a lengthy explanation of how OLS are derived, data generating process and identification (of causes), causal diagrams, back and front doors (a recurrent notion within the book),  treatment effects and a conclusion chapter.

“Unlike statistical research, which is completely made of things that are at least slightly false, statistics itself is almost entirely true.” (p.327)

The second part, called the Toolbox, is closer to a classical introduction to econometrics, albeit with a shortage of mathematics (and no proof whatsoever), although [warning!] logarithms, polynomials, partial derivatives and matrices are used. Along with a consequent (3x) chunk allocated to printed codes, the density of the footnotes significantly increases in this section. It covers an extensive chapter on regression (including testing practice, non-linear and generalised linear models, as well as basic bootstrap without much warning about its use in… regression settings, and LASSO),  one on matching (with propensity scores, kernel weighting, Mahalanobis weighting, one on  simulation, yes simulation! in the sense of producing pseudo-data from known generating processes to check methods, as well as bootstrap (with resampling residuals making at last an appearance!), fixed and random effects (where the author “feels the presence of Andrew Gelman reaching through time and space to disagree”, p.405). The chapter on event studies is about time dependent data with a bit of ARIMA prediction (but nothing on non-stationary series and unit root issues). The more exotic chapters cover (18) difference-in-differences models (control vs treated groups, with John Snow pumping his way in), (19) instrumental variables (aka the minor bane of my 1980’s econometrics courses), with double least squares and generalised methods of moments (if not the simulated version), (20) discontinuity (i.e., changepoints), with the limitation of having a single variate explaining the change, rather than an unknown combination of them, and a rather pedestrian approach to the issue, (iv) other methods (including the first mention of machine learning regression/prediction and some causal forests), concluding with an “Under the rug” portmanteau.

Nothing (afaict) on multivariate regressed variates and simultaneous equations. Hardly an occurrence of Bayesian modelling (p.581), vague enough to remind me of my first course of statistics and the one-line annihilation of the notion.

Duh cover, but nice edition, except for the huge margins that could have been cut to reduce the 622 pages by a third (and harnessed the tendency of the author towards excessive footnotes!). And an unintentional white line on p.238! Cute and vaguely connected little drawings at the head of every chapter (like the head above). A rather terse matter index (except for the entry “The first reader to spot this wins ten bucks“!), which should have been completed with an acronym index.

“Calculus-heads will recognize all of this as taking integrals of the density curve. Did you know there’s calculus hidden inside statistics? The things your professor won’t tell you until it’s too late to drop the class.

Obviously I am biased in that I cannot negatively comment on an author running 5:37 a mile as, by now, I could just compete far from the 5:15 of yester decades! I am just a wee bit suspicious at the reported time, however, given that it happens exactly on page 537… (And I could have clearly taken issue with his 2014 paper, Is Robert anti-teacher? Or with the populist catering to anti-math attitudes as the above found in a footnote!) But I enjoyed reading the conceptual chapter on causality as well as the (more) technical chapter on instrumental variables (a notion I have consistently found confusing all the [long] way from graduate school). And while repeated references are made to Scott Cunningham’s Causal Inference: The Mixtape I think I will stop there with 500⁺ page introductory econometrics books!

[Disclaimer about potential self-plagiarism: this post or an edited version will potentially appear in my Books Review section in CHANCE.]

martingale posteriors

A new Royal Statistical Society Read Paper featuring Edwin Fong, Chris Holmes, and Steve Walker. Starting from the predictive

rather than from the posterior distribution on the parameter is a fairly novel idea, also pursued by Sonia Petrone and some of her coauthors. It thus adopts a de Finetti’s perspective while adding some substance to the rather metaphysical nature of the original. It however relies on the “existence” of an infinite sample in (1) that assumes a form of underlying model à la von Mises or at least an infinite population. The representation of a parameter θ as a function of an infinite sequence comes as a shock first but starts making sense when considering it as a functional of the underlying distribution. Of course, trading (modelling) a random “opaque” parameter θ for (envisioning) an infinite sequence of random (un)observations may sound like a sure loss rather than as a great deal, but it gives substance to the epistemic uncertainty about a distributional parameter, even when a model is assumed, as in Example 1, which defines θ in the usual parametric way (i.e., the mean of the iid variables). Furthermore, the link with bootstrap and even more Bayesian bootstrap becomes clear when θ is seen this way.

Always a fan of minimal loss approaches, but (2.4) defines either a moment or a true parameter value that depends on the parametric family indexed by θ. Hence does not exist outside the primary definition of said parametric family. The following construct of the empirical cdf based on the infinite sequence as providing the θ function is elegant but what is its Bayesian justification? (I did not read Appendix C.2. in full detail but could not spot the prior on F.)

“The resemblance of the martingale posterior to a bootstrap estimator should not have gone unnoticed”

I am always fan of minimal loss approaches, but I wonder at (2.4), as it defines either a moment or a true parameter value that depends on the parametric family indexed by θ. Hence it does not exist outside the primary definition of said parametric family, which limits its appeal. The following construct of the empirical cdf based on the infinite sequence as providing the θ function is elegant and connect with bootstrap, but I wonder at its Bayesian justification. (I did not read Appendix C.2. in full detail but could not spot a prior on F.)

While I completely missed the resemblance, it is indeed the case that, if the predictive at each step is build from the earlier “sample”, the support is not going to evolve. However, this is not particularly exciting as the Bayesian non-parametric estimator is most rudimentary. This seems to bring us back to Rubin (1981) ?! A Dirichlet prior is mentioned with no further detail. And I am getting confused at the complete lack of structure, prior, &tc. It seems to contradict the next section:

“While the prescription of (3.1) remains a subjective task, we find it to be no more subjective than the selection of a likelihood function”

Copulas!!! Again, I am very glad to see copulas involved in the analysis. However, I remain unclear as to why Corollary 1 implies that any sequence of copulas could do the job. Further, why does the Gaussian copula appear as the default choice? What is the computing cost of the update (4.4) after k steps? Similarly (4.7) is using a very special form of copula, with independent-across-dimension increments. I am also missing a guided tour on the implementation, as it sounds explosive in book-keeping and multiplying, while relying on a single hyperparameter in (4.5.2)?

In the illustration section, the use of the galaxy dataset may fail to appeal to Radford Neal, in a spirit similar to Chopin’s & Ridgway’s call to leave the Pima Indians alone, since he delivered a passionate lecture on the inappropriateness of a mixture model for this dataset (at ICMS in 2001). I am unclear as to where the number of modes is extracted from the infinite predictive. What is $\theta$ in this case?

Copulas!!! Although I am unclear why Corollary 1 implies that any sequence of copulas does the job. And why the Gaussian copula appears as the default choice. What is the computing cost of the update (4.4) after k steps? Similarly (4.7) is using a very special form of copula, with independent-across-dimension increments. Missing a guided tour on the implementation, as it sounds explosive in book-keeping and multiplying. A single hyperparameter (4.5.2)?

the most important statistical ideas of the past 50 years

Aki and Andrew are celebrating the New Year in advance by composing a list of the most important statistics ideas occurring (roughly) since they were born (or since Fisher died)! Like

• substitution of computing for mathematical analysis (incl. bootstrap)
• fitting a model with a large number of parameters, using some regularization procedure to get stable estimates and good predictions (e.g., Gaussian processes, neural networks, generative adversarial networks, variational autoencoders)
• multilevel or hierarchical modelling (incl. Bayesian inference)
• advances in statistical algorithms for efficient computing (with a long list of innovations since 1970, including ABC!), pointing out that a large fraction was of the  divide & conquer flavour (in connection with large—if not necessarily Big—data)
• statistical decision analysis (e.g., Bayesian optimization and reinforcement learning, getting beyond classical experimental design )
• robustness (under partial specification, misspecification or in the M-open world)
• EDA à la Tukey and statistical graphics (and R!)
• causal inference (via counterfactuals)

Now, had I been painfully arm-bent into coming up with such a list, it would have certainly been shorter, for lack of opinion about some of these directions (even the Biometrika deputeditoship has certainly helped in reassessing the popularity of different branches!), and I would have have presumably been biased towards Bayes as well as more mathematical flavours. Hence objecting to the witty comment that “theoretical statistics is the theory of applied statistics”(p.10) and including Ghosal and van der Vaart (2017) as a major reference. Also bemoaning the lack of long-term structure and theoretical support of a branch of the machine-learning literature.

Maybe also more space and analysis could have been spent on “debates remain regarding appropriate use and interpretation of statistical methods” (p.11) in that a major difficulty with the latest in data science is not so much the method(s) as the data on which they are based, which in a large fraction of the cases, is not representative and is poorly if at all corrected for this bias. The “replication crisis” is thus only one (tiny) aspect of the challenge.

estimation exam [best of]

Yesterday, I received a few copies of our CRC Press Handbook of Mixture Analysis, while grading my mathematical statistics exam 160 copies. Among the few goodies, I noticed the always popular magical equality

E[1/T]=1/E[T]

that must have been used in so many homeworks and exam handouts by now that it should become a folk theorem. More innovative is the argument that E[1/min{X¹,X²,…}] does not exist for iid U(0,θ) because it is the minimum and thus is the only one among the order statistics with the ability to touch zero. Another universal shortcut was the completeness conclusion that when the integral

was zero for all θ’s then φ had to be equal to zero with no further argument (only one student thought to take the derivative). Plus a growing inability in the cohort to differentiate even simple functions… (At least, most students got the bootstrap right, as exemplified by their R code.) And three stars to the student who thought of completely gluing his anonymisation tag, on every one of his five sheets!, making identification indeed impossible, except by elimination of the 159 other names.

bootstrap in Nature

A news item in the latest issue of Nature I received about Brad Efron winning the “Nobel Prize of Statistics” this year. The bootstrap is certainly an invention worth the recognition, not to mention Efron’s contribution to empirical Bayes analysis,, even though I remain overall reserved about the very notion of a Nobel prize in any field… With an appropriate XXL quote, who called the bootstrap method the ‘best statistical pain reliever ever produced’!