by Roger J.-B. Wets
I first thought I would devote this short contribution to a couple of remarkable technical achievements of David Blackwell and how they influenced subsequent research. This would have included the deep insight provided by his elegant proof of Lyapunov’s theorem about the range of a vector measure, about his seminal articles laying the foundations of dynamic programming, and so on. But it is in his role as a lifelong advisor and model that his influence turned out to be most significant.
It is impossible to find any information about David that does not refer to him as an outstanding teacher, and indeed he was. He liked his classes to be scheduled as early as reasonable. The first course I took with him was an undergraduate course on dynamic programming, in which he mostly covered his own development of the field. It was listed as an undergraduate course, I suppose, on the basis that he didn’t require much more than a decent background in real analysis and linear algebra. But one could never have guessed that it was an undergraduate class on the basis of the student body. There might have been one or two smart undergraduates lost in the audience, but the rest consisted mostly of graduate students in operations research and statistics and a not insignificant number of faculty members. In addition to remembering that homework assignments were extensive, instructive, and relatively hard, I was fascinated by the constructive approach; not just whether it exists or might be done but the fact that the results were derived in such a way that suggested the potential of solution procedures. I didn’t realize at the time how strongly it would eventually influence my own research strategy.
After I took a couple more courses with him and chose to work in stochastic optimization, David became a natural coadvisor of my thesis. The subject stochastic programming (decision making under uncertainty) had been proposed by G. B. Dantzig. I was pleased but not surprised by David’s acceptance to act as coadvisor. But his advice/comments could be quite candid and to the point. The first time I went to discuss what I was planning to do, I gave a too-succinct version of the class of questions I was going to consider, and David bluntly told me “but that’s just finding the minimum of an expected function”, and he definitely was not impressed. When, a bit later, I explained that this “function” was not a simple one but involved not just an objective but also (complex) constraints, he revised his assessment to “Oh, that, make sure you first handle some manageable cases”, and he immediately started with a couple of suggestions that eventually turned up as illustrations in my thesis.
He had played, more than once, the role of the “wise uncle” for students interested in optimization who were concerned about getting a degree in a field whose mathematical standing wasn’t yet well established or recognized. They somehow felt that they could confide their concerns to him and would then receive the appropriate advice. He could be quite plainspoken in such situations and simply told the hesitating student, “You are telling me that you are interested in area A, but would consider getting a degree in statistics, how can this make sense?” For one of my friends, this advice turned out to be exactly what was needed, and it resulted in a brilliant, mathematically rich career.
I didn’t return to statistics until it became difficult to ignore the ubiquitous lack of statistical data available to construct reliably the distribution of the random quantities of a stochastic optimization problem. My approach was based on the idea of incorporating in the estimation problem all the information available about the stochastic phenomena, not just the observed data but also all nondata information that might be available, and relying on variational analysis for the theoretical foundations and optimization techniques to derive nonparametric, as well as parametric, estimates. This didn’t look like an easy sale to either frequentist or Bayesian statisticians. So, I went to see David, by then professor emeritus. After all, this could be fitted in the framework of the theory of games and statistical decisions. This time, it didn’t take him more than a few minutes to understand and encourage me to pursue this approach. Of course, he also immediately suggested further possibilities and reserved a place for a lecture in the Neyman Seminar, as well as time for further discussions.
On repeated occasions, David provided this steady anchor that made you feel that what you were trying to do was or was not worthwhile, and, given the wide scope of his interests and knowledge, this always turned out to be an invaluable resource. Thanks, professor extraordinaire, David Blackwell.
