Statistical Science

A conversation with Milton Sobel

Nitis Mukhopadhyay

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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.

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Statist. Sci., Volume 15, Number 2 (2000), 168-190.

First available in Project Euclid: 24 December 2001

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Mukhopadhyay, Nitis. A conversation with Milton Sobel. Statist. Sci. 15 (2000), no. 2, 168--190. doi:10.1214/ss/1009212756.

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  • Anderson, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist. 31 165-197.
  • Bechhofer, R. E., Kiefer, J. and Sobel, M. (1968). Sequential Identification and Ranking Procedures. Univ. Chicago Press.
  • Bickel, P. J. and Doksum, K. J. (1977). Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day, San Francisco, CA.
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  • 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.
  • 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.
  • 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.
  • Khan, R. A. (1973). On sequential distinguishability. Ann. Statist. 1 838-850.
  • 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.
  • 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.]
  • 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.]
  • 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.
  • Wald, A. (1950). Statistical Decision Functions. Wiley, New York.