#### 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.