Source: Statist. Sci.
Volume 15, Number 2
Milton Sobel was born in New York City on August 30, 1919. He earned
his B.A. degree in mathematics from the City College of New York in 1940, an
M.A. degree in mathematics and a Ph.D. degree in mathematical statistics from
Columbia University in 1946 and 1951, respectively. His Ph.D. thesis advisor
was Abraham Wald. He has made substantial contributions in several areas of
statistics and mathematics—including decision theory, sequential
analysis, selection and ranking, reliability analysis, combinatorial problems,
Dirichlet processes, as well as statistical tables and computing. He has been
particularly credited for path breaking contributions in selection and ranking,
sequential analysis and reliability, includingthe landmark book, Sequential
Identi fication and Ranking Procedures (1968), coauthored with Robert E.
Bechhofer and Jack C. Kiefer. Later, he collaborated with Jean D.Gibbons and
Ingram Olkin to write a methodologically oriented book, Selecting and Ordering
Populations (1977), on the subject. He has published authoritative books on
Dirichlet distributions, Type 1 and Type 2 with V. R. R.Uppuluri and K.
Frankowski. He is the author or coauthor of more than one hundred and twenty
research publications, many of which are part of today ’s statistical
folklore. During the period July 1940 through June 1960, his career path led
him to work at the Census Bureau, the Army War College (Fort McNair),Columbia
University, Wayne State University, Cornell University and Bell Laboratories.
From September 1960 through June 1975, he was Professor of Statistics at the
University of Minnesota, and from July 1975 through June 1989 he was a
Professor in the Department of Probability and Statistics at the University of
California at Santa Barbara. He has since been a Professor Emeritus at UC Santa
Barbara. He has earned many honors and awards, including Fellow of the
Institute of Mathematical Statistics (1956) and Fellow of the American
Statistical Association (1958),a Guggenheim Fellowship (1967 –1968), a
NIH Fellowship (1968 –1969)and elected membership in the International
Statistical Institute (1974). He continues to think and work harder than many
half his age and still goes to his department at UC Santa Barbara every day.
Milton Sobel remains vigorous in attacking and solving hard problems.
Anderson, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist. 31 165-197.
Mathematical Reviews (MathSciNet): MR116441
Bechhofer, R. E., Kiefer, J. and Sobel, M. (1968). Sequential Identification and Ranking Procedures. Univ. Chicago Press.
Mathematical Reviews (MathSciNet): MR245133
Bickel, P. J. and Doksum, K. J. (1977). Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day, San Francisco, CA.
Mathematical Reviews (MathSciNet): MR443141
Chow, Y. S. and Robbins, H. (1965). On the asymptotic theory of fixed-width sequential confidence intervals for the mean. Ann. Math. Statist. 36 457-462.
Mathematical Reviews (MathSciNet): MR172423
Courant, R. and Robbins, H. (1941). What is Mathematics? Oxford Univ. Press.
Mathematical Reviews (MathSciNet): MR3,144b
Dudewicz, E. and Mishra, S. N. (1988). Modern Mathematical Statistics. Wiley, New York.
Epstein, B. and Sobel, M. (1953). Life testing. J. Amer. Statist. Assoc. 48 486-502.
Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testingfrom an exponential distribution. Ann. Math. Statist. 25 373-381.
Epstein, B. and Sobel, M. (1955). Sequential procedures in life testingfrom an exponential distribution. Ann. Math. Statist. 26 82-93.
Mathematical Reviews (MathSciNet): MR67431
Feller, W. (1950), (1968). An Introduction to Probability Theory and Its Applications 1, 1st and 3rd ed. Wiley, New York.
Ghosh, B. K. and Sen, P. K. (eds.) (1991). Handbook of Sequential Analysis. Dekker, New York.
Gibbons, J. D., Olkin, I. and Sobel, M. (1977). Selecting and Ordering Populations. Wiley, New York.
Mathematical Reviews (MathSciNet): MR488441
Katz, L. and Sobel, M. (1970). Coverage of generalized chess boards by randomly placed rooks. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 3 555-564, Univ. California Press, Berkeley.
Mathematical Reviews (MathSciNet): MR396305
Khan, R. A. (1973). On sequential distinguishability. Ann. Statist. 1 838-850.
Mathematical Reviews (MathSciNet): MR345355
McCabe, G. P., Jr. (1973). Estimation of the number of terms in a sum. J. Amer. Statist. Assoc. 68 452-456.
Parzen, E. (1960). Modern Probability Theory and Its Applications. Wiley, New York.
Robbins, H. (1970). Sequential estimation of an integer mean. In Scientists at Work. Festschrift Honoring Herman Wold (T. Dalenius et al., eds.) 205-210. Almqvist and Wiksells, Uppsala.
Robbins, H., Sobel, M. and Starr, N. (1968). A sequential procedure for selectingthe best of k populations. Ann. Math. Statist. 24 319-337.
Mathematical Reviews (MathSciNet): MR223019
Sobel, M. (1953). An essentially complete class of decision functions for certain standard sequential problems. Ann. Math. Statist. 24 319-337.
Sobel, M. (1956). Statistical techniques for reducingexperiment time in reliability. Bell System Technical J. 36 179-202.
Sobel, M. and Frankowski, K. (1994). The 500th anniversary of the sharingproblem (The oldest problem in the theory of probability). Amer. Math. Monthly. 101 833-847.
Sobel, M. and Groll, P. A. (1959). Group testingto eliminate efficiently all defectives in a binomial sample. Bell System Technical J. 38 1179-1252.
Sobel, M., Uppuluri, V. R. R. and Frankowski, K. (1977). Dirichlet Distributions-Type 1. Amer. Math Soc., Washington, DC. [Also, in Selected Tables in Mathematical Statistics 4. IMS, Hayward, CA.]
Mathematical Reviews (MathSciNet): MR423747
Sobel, M., Uppuluri, V. R. R. and Frankowski, K. (1985). Dirichlet Integrals of Type 2 and Their Applications. Amer. Math. Soc., Washington, DC. [Also, in Selected Tables in Mathematical Statistics 9. IMS, Hayward, CA.]
Mathematical Reviews (MathSciNet): MR796797
Sobel, M. and Wald, A. (1949). A sequential decision procedure for choosingone of three hypotheses concerningthe unknown mean of a normal distribution. Ann. Math. Statist. 20 502- 522.
Wald, A. (1947). Sequential Analysis. Wiley, New York.
Mathematical Reviews (MathSciNet): MR8,593h
Wald, A. (1950). Statistical Decision Functions. Wiley, New York.