Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by David Brillinger

I am one of the many whose ca­reers and lives Dav­id Black­well in­flu­enced in im­port­ant ways.

My first con­tact with Dav­id was in 1958. I bought a copy of the Black­well and Gir­shick (1954) book us­ing part of my Put­nam Prize money. From that work I learned the de­cision the­ory and Bayesian ap­proaches to stat­ist­ic­al prob­lems. I also re­mem­ber lik­ing the group the­ory ma­ter­i­al.

My next con­tact with Dav­id came in spring 1961. He tele­phoned me at Prin­ceton in­vit­ing me to Berke­ley. The con­ver­sa­tion ended with “If ever …” I didn’t ac­cept the in­vit­a­tion then as I had a postdoc­tor­al fel­low­ship to spend the fol­low­ing year in Lon­don, but I did not for­get it. What happened even­tu­ally is that I be­came a lec­turer and then a read­er at the Lon­don School of Eco­nom­ics (LSE) for most of the 1960s. I did fol­low Dav­id’s work, and I did think about Berke­ley from time to time. One thing that I no­ticed was that Dav­id was typ­ic­ally spoken of with awe both in the United King­dom and United States. I par­tic­u­larly re­mem­ber that, in the mid-1960s, I went through Dav­id’s 1951 pa­per “The range of cer­tain vec­tor in­teg­rals” when I was pre­par­ing a 1967 Pro­ceed­ings of the AMS pa­per, “Bounded poly­meas­ures and as­so­ci­ated trans­la­tion com­mut­at­ive poly­no­mi­al op­er­at­ors”.

Dur­ing the aca­dem­ic peri­od 1967–1968, I spent nine months in Berke­ley’s Stat­ist­ics De­part­ment on sab­bat­ic­al leave from LSE. I found Dav­id to be lar­ger than life, and also I fi­nally met a non­ag­gress­ive Bayesian! Just after that vis­it he fur­ther helped my ca­reer when he com­mu­nic­ated my 1969 pa­per, “An asymp­tot­ic rep­res­ent­a­tion of the sample dis­tri­bu­tion func­tion”, to the Bul­let­in of the AMS.

I be­came Dav­id’s col­league in Janu­ary 1970 when I joined the Berke­ley fac­ulty. There his col­legi­al­ity, teach­ing, re­search, power-packed talks, com­mit­tee work, treat­ment of stu­dents, and so­cial con­science were role mod­els for aca­dem­ic be­ha­vi­or. To men­tion one per­son­al re­search ex­ample, his work with Lester Du­bins that ap­peared in the 1983 Pro­ceed­ings of the AMS, “An ex­ten­sion of Skorok­hod’s al­most sure rep­res­ent­a­tion the­or­em”, surely in­flu­enced my 1980 work, “Ana­lys­is of vari­ance prob­lems un­der time series mod­els”, Hand­book of Stat­ist­ics 1. In that pa­per Skorok­hod rep­res­ent­a­tion res­ults al­lowed form­al de­vel­op­ment of asymp­tot­ic non­cent­ral chi-squared and \( F \) dis­tri­bu­tions for vari­ous time series stat­ist­ics.

Dav­id Black­well has been there my whole aca­dem­ic life, and his con­tri­bu­tions and style re­main. It was a priv­ilege to share con­ver­sa­tions and ex­per­i­ences with him, for he was a ma­jor reas­on why I came to Berke­ley. He helped me out con­tinu­ally when I was de­part­ment chair.

I wish to end by men­tion­ing that, in an en­counter, Dav­id seemed al­ways to have a pun­gent quip to of­fer. One I re­mem­ber from the early 1980s is “Ron­ald Re­agan likes strong trade uni­ons — in Po­land.”