Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by Herman Chernoff

I first met Dav­id Black­well in 1951 when we were both in­vited to vis­it the new Stan­ford Uni­versity De­part­ment of Stat­ist­ics. By then he was a re­cog­nized force in stat­ist­ics, hav­ing con­trib­uted the Rao–Black­well the­or­em on the use of suf­fi­cient stat­ist­ics to de­rive ef­fi­cient un­biased es­tim­ates and the Ar­row–Black­well–Gir­shick de­riv­a­tion of the op­tim­al­ity of the se­quen­tial prob­ab­il­ity ra­tio test.

The lat­ter de­riv­a­tion was based on a plan pro­posed by Wald and Wolfow­itz, the de­tails of which suffered from a ser­i­ous meas­ur­ab­il­ity dif­fi­culty. Ar­row, Black­well, and Gir­shick by­passed that prob­lem by em­ploy­ing a back­ward in­duc­tion ar­gu­ment, the suc­cess of which de­pended on the fact that a de­cision to be made in the dis­tant fu­ture would have a neg­li­gible ef­fect on the cur­rent ex­pec­ted value of the over­all strategy. This back­ward in­duc­tion ar­gu­ment was es­sen­tially the ori­gin of dy­nam­ic pro­gram­ming. Black­well used to claim that se­quen­tial ana­lys­is and dy­nam­ic pro­gram­ming were the same sub­ject.

At the time we met, Dav­id and his wife Ann already had five of their eight chil­dren. Trans­port­ing his fam­ily by car across coun­try was a ma­jor chal­lenge re­quir­ing con­sid­er­able dis­cip­line and plan­ning at a time when pro­fess­or­i­al salar­ies were ex­tremely lim­ited. We were dis­ap­poin­ted when Dav­id chose to go to Berke­ley rather than to Stan­ford.

Ann and I had a vice in com­mon. We both loved ice cream. My wife Judy no­ticed that at pic­nics, Ann had a def­in­ite tend­ency to over­count the con­sumers, as a res­ult of which we al­ways had an ex­tra por­tion, which Ann would grace­fully con­sume to avoid a battle among her chil­dren.

I have known many very smart people, in­clud­ing some No­bel laur­eates, but Dav­id had the greatest abil­ity to take a com­plic­ated situ­ation, sci­entif­ic or per­son­al, and ex­plain the is­sues clearly and simply. This gift made him a great ex­pos­it­or and ad­visor. His book, Ba­sic Stat­ist­ics, was an ex­traordin­ary il­lus­tra­tion of his abil­ity to clearly and con­cisely ex­plain the sub­ject to be­gin­ners.

We had one ma­jor mis­un­der­stand­ing. He main­tained that I had in­tro­duced him to the sec­ret­ary prob­lem, and I just as dis­tinctly claim that he had in­tro­duced me to it. Judy and I both en­joyed vis­it­ing with Dav­id and Ann, and we were honored to be in­vited by Dav­id to the spe­cial din­ner Har­vard had for its re­cip­i­ents of the hon­or­ary doc­tor­ate.