Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by John Rolph

I was a stat­ist­ics gradu­ate stu­dent at Berke­ley in the mid-1960s. It was my good for­tune that Dav­id Black­well taught the in­fer­ence course to the first-year stu­dents in my co­hort. I was so taken with him and his teach­ing that I sub­sequently en­rolled in vir­tu­ally every course he taught. They em­braced a dizzy­ing ar­ray of top­ics, ran­ging from in­form­a­tion the­ory to game the­ory to sem­inars on dy­nam­ic pro­gram­ming, ban­dit prob­lems, search, and re­lated top­ics. In his teach­ing as in his re­search, his in­terests and know­ledge were broad.

Dav­id Black­well was a teach­er without par­al­lel. I was par­tic­u­larly im­pressed by how he could make truly deep con­cepts trans­par­ent — even to the be­gin­ner. In­deed, the depth was such that un­der­stand­ing some­times blos­somed mys­ter­i­ously and gradu­ally. I re­call go­ing over class notes after class and only then be­gin­ning to un­der­stand how deep and subtle some of the con­cepts he had presen­ted were. To make sure we un­der­stood the ideas, a group that in­cluded Steve Sti­gler, Bruce Hoad­ley, and me made a prac­tice of as­sign­ing two to take notes and one to listen in­tently to his lec­tures. We would meet af­ter­ward, re­con­struct­ing the lec­tures to make sure we all ac­tu­ally un­der­stood the con­cepts and res­ults he covered.

Un­like most fac­ulty mem­bers who spe­cial­ized in one or per­haps two areas, Black­well was a man of re­mark­ably di­verse in­terests; thus his stu­dents worked on a wide vari­ety of top­ics. While I was there, he su­per­vised dis­ser­ta­tions in in­form­a­tion the­ory, dy­nam­ic pro­gram­ming, game the­ory, Bayesian in­fer­ence, search the­ory, prob­ab­il­ity the­ory, stochast­ic pro­cesses, and stop­ping rules. He moved from stu­dent to stu­dent and hence top­ic to top­ic with as­ton­ish­ing flex­ib­il­ity and fo­cus.

To say he was a quick study is a re­mark­able un­der­state­ment. When you met with him, he would look over what you had done, ask a few prob­ing ques­tions, sug­gest an ap­proach or two to your cur­rent prob­lem, and send you on your way. These ses­sions typ­ic­ally ran ten to twenty minutes. In­deed, when I fi­nally brought him a draft of what I hoped was my com­pleted dis­ser­ta­tion, he read it, asked a few pen­et­rat­ing ques­tions, listened to my re­sponses, then told me I was fin­ished — all in a half hour! This mod­us op­erandi ob­vi­ously worked splen­didly — he su­per­vised sixty-five doc­tor­al stu­dents dur­ing his ca­reer.

Al­though Dav­id Black­well had strong be­liefs and points of view, he was not an avid pros­elyt­izer. In­deed, it was only gradu­ally that I came to un­der­stand and ap­pre­ci­ate that Dav­id Black­well was the lone Bayesian in the Berke­ley Stat­ist­ics De­part­ment. In­ter­est­ingly, the con­tent of the first-year in­fer­ence course he taught us was very sim­il­ar to the course Erich Lehmann cus­tom­ar­ily gave — Bayes es­tim­ates only came up as a con­veni­ent math­em­at­ic­al concept, not as a philo­sophy of in­fer­ence. That Black­well was not a vo­ci­fer­ous pro­ponent of his be­lief in the su­peri­or­ity of the Bayesian ap­proach was typ­ic­al of his non­con­front­a­tion­al way of in­ter­act­ing with his col­leagues.

Dav­id Black­well was a man we shall all re­mem­ber with great re­spect and af­fec­tion. He was a man of mod­est de­mean­or who would solve seem­ingly in­tract­able prob­lems with math­em­at­ic­al rig­or, el­eg­ance, and trans­par­ency. The im­pact of his re­search was both sub­stan­tial and broad. And he treated his stu­dents as equals, both help­ing them and chal­len­ging them to be suc­cess­ful in their re­search. He was a per­son of ex­traordin­ary char­ac­ter and abil­ity; it was a priv­ilege to know him and to learn from him.