Francisco J. Samaniego
Because of David Blackwell’s widely recognized genius, as evidenced in his path-breaking research, the many creative ideas he generously shared with students and colleagues, his election to the National Academy of Sciences, and his receipt of the coveted Berkeley Citation upon his formal retirement from the faculty, it is perhaps understandable that another facet of his remarkable career would be less known and less universally celebrated. This facet was his extraordinary ability to teach mathematics and statistics in new, clear, and compelling ways. There is a good deal of evidence that may be advanced in support of the proposition that Blackwell was an exceptional teacher. We would be remiss if this aspect of his wonderfully successful career was overlooked in the present overview of his work. While our discussion of Blackwell’s teaching is necessarily brief, we hope that we will leave no doubt among readers of this piece that Blackwell was a preeminent teacher and mentor.
The most telling evidence of Blackwell’s teaching prowess is simply the testimonials from students and colleagues that exist in a number far too great to attempt a comprehensive summary. Suffice it to say that many of his students considered him to be the finest instructor that they ever had the privilege to study with. His style was unfailingly engaging, as it was his custom to share his natural curiosity with his students, explaining not just the “how” associated with a statistical procedure but the “why” as well, along with the motivation for the ideas involved and the (often surprising) connections with other ideas usually of interest in their own right. It was a pleasure to hear him speak. One generally came away from a lecture by David Blackwell both impressed with his mastery of the subject and intrigued by questions he had left his audience to think about. His colleagues at Berkeley looked to him as a model and often sought his advice on the best way to present a given topic (as well as on a host of other matters, personal and professional). In spite of his wonderful gifts as a teacher, Blackwell was very modest about his skills and would give his advice as if it was a tentative, off-the-cuff suggestion. Once, in a reception prior to a seminar he presented at UC Davis, a former student of his asked him, “David, what do you do when you’ve presented an idea in a way that you consider to be ‘just right’, and a student raises his hand and says ‘I didn’t get that’?” Without missing a beat, David answered, “Well, I just repeat exactly what I just said, only louder.”
David Blackwell’s well-honed teaching instincts were as evident in his writings as they were in the classroom. Two of his many published “notes” come to mind in this regard. These notes appeared in the Annals of Statistics volume in which Thomas Ferguson presented his now celebrated paper on Bayesian nonparametrics (an idea, by the way, that he acknowledged as grounded in his discussions with Blackwell). In a note entitled “Discreteness of Ferguson Selections”, Blackwell gave an elementary proof of the discreteness of draws from a Dirichlet process, shedding much light on this particular characteristic of Dirichlet processes (which had been proven by Ferguson in an Annals of Probability paper using much more complex arguments). In the same AoP issue, Blackwell and MacQueen presented an alternative derivation of the Dirichlet process using a lovely and quite intuitive construction involving Pólya urn schemes. The latter paper has led to much fruitful research in Bayesian nonparametrics. Both papers contained useful techniques, but their greatest contribution was, without doubt, the clarification of the properties and potential of Ferguson’s Dirichlet process.
Blackwell published the elementary textbook Basic Statistics in 1969. The book is unique in the field and is recommended reading both for students just being exposed to the subject and, we dare say, for the statistics community as a whole. It is no exaggeration to refer to the book as a “gem”. In the book, Blackwell covered the “standard topics” found in an introductory course — elementary probability, the binomial and normal models, correlation, estimation, prediction, and the chi-square test for association. The treatment of these topics was, however, fresh and crisp, with most of the ideas motivated by thinking about drawing balls from urns. For example, he chose to introduce the idea of Bayesian point estimation through the problem of estimating the number of fish in a pond via a mark-recapture experiment. Although the mathematical level of the book was intentionally low, the conceptual reach was much broader than what one usually finds at the introductory level. In his preface, Blackwell describes his approach as “intuitive, informal, concrete, decision-theoretic and Bayesian”. He took on the notions of probability densities, mean squared error, multiple correlation, prior distributions, point estimation, and the normal and chi-square approximations, all with the very modest expectation that the students reading the book “could do arithmetic, substitute in simple formulas, plot points and draw a smooth curve through plotted points”. He was true to his promise of making statistics accessible to anyone who had only these skills. Perhaps the most remarkable thing about this book is that Blackwell managed to pack a treasure trove of ideas into 138 pages, divided into sixteen chapters and containing 118 problems and their solutions. He had a gift for getting to the core of the topics he wrote or taught about. This book is a lovely example of that gift in action.
