by Albert Lo
David Blackwell wrote one of the first comprehensive treatments of Bayesian statistics, and his insistence on the Bayesian approach is legendary. I approached Blackwell for a Ph.D. thesis topic in the mid-1970s. He told me to look in the Annals of Statistics, find a topic I liked, and come back. After some searching, I reported that kernel density estimation interested me. Blackwell, staring at me with his piercing big eyes, said “The topic is fine, yet it must be done the Bayesian way.” This was exactly what he said to me. Later, when I presented to him a result on the consistency of the posterior distribution of a location parameter with respect to a Lebesgue prior, he concluded matter-of-factly, “It is good since it is almost Bayesian.” Again, these were his exact words. On another occasion he stated that all the non-Bayesian papers in the Annals have to be rewritten using a Bayesian approach, and I myself found this “Bayesianization” a good source of research topics.
Blackwell always insisted on the exactness and clarity of solution. For all his undoubted mathematical ability, his preference was for simplicity over mathematical abstraction. On the density estimation problem, he suggested modeling a density by a location mixture of uniform kernels and putting a Dirichlet process prior on the mixing distribution. The problem was hard then, and after a year and a half of futile searching, I had to present an alternative, yet more standard, approach based on expanding the square root of the density in an orthogonal series with a prior on the infinite sequence of coefficients that lies on the shell of a Hilbert sphere. Upon hearing the proposed approach, Blackwell simply commented “Al, you are not ready.” To this day, I can still hear his devastating voice! His opinion about the maturity/readiness of students was perceptive; two years later his Bayesian mixture density problem was resolved with an explicit solution that he had anticipated, presumably at a time when the student was ready.
Though there are suggestions of a good-natured rivalry between Blackwell and some of his famous colleagues, he was not one for direct confrontation. He was very quiet about the racial injustice that he endured and overcame, never mentioning the subject in my hearing. It brings to mind how he handled me as a student, who had been expertly trained by Berkeley frequentists. His only advice to me on how to learn Bayesian statistics was to read Part III of De Groot’s text. Though he made some extremely valuable suggestions in his nice and gentlemanly way, he never really discussed or showed me how to approach a research problem, except by example. I had to find my own way by observing him and others (mostly others) in the department. The discrimination Blackwell experienced may have given him the philosophy that one should also be able to fight his own way up, or perhaps that if one is worthy, one will eventually be able to make it on one’s own. Or perhaps he understood that this was the right approach to take with certain students individually.
David Blackwell was an intellectual giant. But he was modest and unassuming on a personal level. He always dressed properly in an aged jacket/suit, and he drove an old car that often invited jokes from students. While graduate students all over the world were learning about the Rao–Blackwell theorem, I never saw him teaching a graduate course. He enjoyed teaching undergraduate courses, and he placed great emphasis upon spending time on preparation to improve classroom teaching.
A great mind and a great spirit has departed. The world is a richer place because of his writings, but those of us who had the privilege of meeting him personally have benefited even more.
