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Professor Blackwell at 80

RESEARCH

Dr. David Blackwell has published over 90 papers and books in various areas of mathematics; for a near complete listing see Mathematics Reviews at Math Scinet. As they worked in the same area, it is curious whether the three African American statisticians Charles Bell , Albert Turner Bharucha-Reid, and David Blackwell collaborated. I know of just one joint project of two: Bell, C. B.; Blackwell, David; Breiman, Leo On the completeness of order statistics . Ann. Math. Statist. 31 1960 794--797.

David Blackwell has contributed to several areas in mathematics: dynamic programming, game theory, measure theory, probability theory, set theory, and mathematical statistics. The Rao-Blackwell Theorem is well known in statistics. The Blackwell Renewal Theorem (see [1] & [2]) really defines renewal theory, and introduced the Lusin spaces now known as Blackwell spaces.Three of his favorite papers of his own work are:

1. Blackwell, David On an equation of Wald , Ann. Math. Statistics 17, (1946). 84--87.

2. Arrow, K. J.; Blackwell, D.; Girshick, M. A. Bayes and minimax solutions of sequential decision problems . Econometrica 17, (1949). 213--244.

3. Blackwell, David Infinite games and analytic sets , Proc. Nat. Acad. Sci. U.S.A. 58 1967 1836--1837.

Statistics, probability and game theory. Papers in honor of David Blackwell , Edited by T. S. Ferguson, L. S. Shapley and J. B. MacQueen. Institute of Mathematical Statistics Lecture Notes---Monograph Series, 30. Institute of Mathematical Statistics, Hayward, CA, 1996. xiv+407 pp. ISBN: 0-940600-42-0 60-06

Books by Blackwell:

Blackwell, David; Girshick, M. A. Theory of games and statistical decisions, Reprint of the 1954 (John Wiley and sons) edition. Dover Publications, Inc., New York, 1979. xi+355 pp. ISBN: 0-486-63831-6.

Selected Papers by Blackwell:

80. Blackwell, David; Diaconis, Persi A non-measurable tail set. Statistics, probability and game theory, 1--5, IMS Lecture Notes Monogr. Ser., 30, Inst. Math. Statist., Hayward, CA, 1996. 28A05

79. Blackwell, D. Large deviations for martingales. Festschrift for Lucien Le Cam, 89--91, Springer, New York, 1997.

78. Blackwell, D. Minimax vs. Bayes prediction. Probab. Engrg. Inform. Sci. 9 (1995), no. 1, 53--58.

77. Blackwell, David Operator solution of infinite $G\sb \delta$ games of imperfect information, Probability, statistics, and mathematics, 83--87, Academic Press, Boston, MA, 1989.

76. Blackwell, D.; Ramakrishnan, S. Stationary plans need not be uniformly adequate for leavable, Borel gambling problems. Proc. Amer. Math. Soc. 102 (1988), no. 4, 1024--1027.

75. Blackwell, David; Mauldin, R. Daniel Ulam's redistribution of energy problem: collision transformations. Lett. Math. Phys. 10 (1985), no. 2-3, 149--153.

74. Blackwell, David; Dubins, Lester E. An extension of Skorohod's almost sure representation theorem. Proc. Amer. Math. Soc. 89 (1983), no. 4, 691--692.

73. Blackwell, David; Maitra, Ashok Factorization of probability measures and absolutely measurable sets, Proc. Amer. Math. Soc. 92 (1984), no. 2, A Festschrift for Erich L. Lehmann, pp. 79--82, Wadsworth Statist./Probab. Ser., Wadsworth, Belmont, Calif., 1983.

72. Blackwell, D.; Ramamoorthi, R. V. A Bayes but not classically sufficient statistic, Ann. Statist. 10 (1982), no. 3, 1025--1026.

71. Blackwell, D. There are no Borel SPLIFs, Ann. Probab. 8 (1980), no. 6, 1189--1190.

70. Blackwell, D. Borel sets via games, Ann. Probab. 9 (1981), no. 2, 321--322.

69. Blackwell, D. Borel-programmable functions, Ann. Probability 6 (1978), no. 2. 321--324.

68. Blackwell, David On stationary policies. With discussion, J. Roy. Statist. Soc. Ser. 133 (1970), no. 1, 33--37.

67. Blackwell, David The stochastic processes of Borel gambling and dynamic programming, Ann. Statist. 4 (1976), no. 2, 370--374. 60G05 (49C15)

66. Blackwell, David; Dubins, Lester E. On existence and non-existence of proper, regular, conditional distributions, Ann. Probability 3 (1975), no. 5, 741--752.

65. Blackwell, David; MacQueen, James B. Ferguson distributions via P-lya urn schemes, Ann. Statist. 1 (1973), 353--355.

64. Blackwell, D.; Freedman, D.; Orkin, M. The optimal reward operator in dynamic programming, Ann. Probability 2 (1974), 926--941.

63. Blackwell, David; Freedman, David On the amount of variance needed to escape from a strip, Ann. Probability 1 (1973), 772--787.

62. Blackwell, David Discreteness of Ferguson selections, Ann. Statist. 1 (1973), 356--358.

61. Blackwell, D. Infinite $G\sb{\delta }$-games with imperfect information, Zastos. Mat. 10 1969 99--101.

60. Blackwell, David; Dubins, Lester An elementary proof of an identity of Gould's, Bol. Soc. Mat. Mexicana (2) 11 1966 108--110.

59. Blackwell, David; Freedman, David On the local behavior of Markov transition probabilities, Ann. Math. Statist. 39 1968, 2123--2127.

58. Blackwell, David A Borel set not containing a graph, Ann. Math. Statist. 39 1968 1345--1347.

57. Blackwell, David; Ferguson, T. S. The big match , Ann. Math. Statist 39 1968 159--163.

56. Blackwell, David Infinite games and analytic sets , Proc. Nat. Acad. Sci. U.S.A. 58 1967 1836--1837.

55. Bickel, Peter J.; Blackwell, David A note on Bayes estimates . Ann. Math. Statist. 38 1967 1907--1911.

54. Blackwell, David Positive dynamic programming . 1967 Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. I: Statistics pp. 415--418 Univ. California Press, Berkeley, Calif.

53. Blackwell, David; Kendall, David The martin boundary of P-lya's urn scheme, and an application to stochastic population growth . J. Appl. Probability 1 1964 284--296.

52. Blackwell, David Discounted dynamic programming . Ann. Math. Statist. 36 1965 226--235.

51. Blackwell, David; Freedman, David A remark on the coin tossing game . Ann. Math. Statist 35 1964 1345--1347.

50. Blackwell, D.; Deuel, P.; Freedman, D. The last return to equilibrium in a coin-tossing game . Ann. Math. Statist 35 1964 1344.

49. Blackwell, David; Freedman, David The tail $\sigma$-field of a Markov chain and a theorem of Orey . Ann. Math. Statist. 35 1964 1291--1295.

48. Blackwell, David Probability bounds via dynamic programming . 1964 Proc. Sympos. Appl. Math., Vol. XVI pp. 277--280 Amer. Math. Soc., Providence, R.I.

47. Blackwell, David Memoryless strategies in finite-stage dynamic programming, Ann. Math. Statist. 35 1964 863--865.

46. Blackwell, David; Dubins, Lester E. A converse to the dominated convergence theorem, Illinois J. Math. 7 1963 508--514.

45. Blackwell, David Discrete dynamic programming, Ann. Math. Statist. 33 1962 719--726.

44. Blackwell, David; Dubins, Lester Merging of opinions with increasing information, Ann. Math. Statist. 33 1962 882--886.

43. Blackwell, David; Dubins, Lester E. Sharp bounds on the distribution of the Hardy-Littlewood maximal function, Proc. Amer. Math. Soc. 14 1963 450--453.

42. Blackwell, D.; Ryll-Nardzewski, C. Non-existence of everywhere proper conditional distributions, Ann. Math. Statist. 34 1963 223--225.

41. Blackwell, David Minimax and irreducible matrices . J. Math. Anal. Appl. 3 1961 37--39.

40. Blackwell, David Exponential error bounds for finite state channels . 1961 Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I pp. 57--63 Univ. California Press, Berkeley, Calif.

39. Blackwell, David Information theory . 1961 Modern mathematics for the engineer: Second series pp. 182--193 McGraw-Hill, New York

38. Bell, C. B.; Blackwell, David; Breiman, Leo On the completeness of order statistics, Ann. Math. Statist. 31 1960 794--797

37. Blackwell, David; Breiman, Leo; Thomasian, A. J. The capacity of a certain channel classes under random coding . Ann. Math. Statist. 31 1960 558--567.

36. Blackwell, David; Breiman, Leo; Thomasian, A. J. The capacity of a class of channels . Ann. Math. Statist. 30 1959 1229--1241.

35. Blackwell, David Infinite codes for memoryless channels . Ann. Math. Statist. 30 1959 1242--1244.

34. Blackwell, David On the functional equation of dynamic programming , J. Math. Anal. Appl. 2 1961 273--276.

33. Blackwell, David; Breiman, Leo; Thomasian, A. J. Proof of Shannon's transmission theorem for finite-state indecomposable channels . Ann. Math. Statist. 29 1958 1209--1220.

32. Blackwell, David; Hodges, J. L., Jr. The probability in the extreme tail of a convolution . Ann. Math. Statist. 30 1959 1113--1120.

31. Blackwell, David The entropy of functions of finite-state Markov chains . 1957 Transactions of the first Prague conference on information theory, Statistical decision functions, random processes held at Liblice near Prague from November 28 to 30, 1956 pp. 13--20 Publishing House of the Czechoslovak Academy of Sciences, Prague

30. Blackwell, David; Koopmans, Lambert On the identifiability problem for functions of finite Markov chains . Ann. Math. Statist. 28 1957 1011--1015.

29. Blackwell, David Another countable Markov process with only instantaneous states . Ann. Math. Statist 29 1958 313--316.

28. Blackwell, David; Hodges, J. L., Jr. Design for the control of selection bias . Ann. Math. Statist. 28 (1957), 449--460.

27. Blackwell, David On discrete variables whose sum is absolutely continuous . Ann. Math. Statist. 28 (1957), 520--521.

26. Blackwell, David Controlled random walks . Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, pp. 336--338. Erven P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam, 1956.

25. Blackwell, David On a class of probability spaces . Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954--1955, vol. II, pp. 1--6. University of California Press, Berkeley and Los Angeles, 1956.

24. Blackwell, David An analog of the minimax theorem for vector payoffs . Pacific J. Math. 6 (1956), 1--8.

23. Blackwell, David On transient Markov processes with a countable number of states and stationary transition probabilities . Ann. Math. Statist. 26 (1955), 654--658.

22. Blackwell, David; Bowker, Albert H. Obituary: Meyer Abraham Girshick, 1908--1955. Ann. Math. Statist. 26, (1955). 365--367.

21. Blackwell, David On multi-component attrition games . Naval Res. Logist. Quart. 1 (1954), 210--216 (1955).

20. Blackwell, David On optimal systems. Ann. Math. Statistics 25, (1954). 394--397.

21. Blackwell, David A representation problem. Proc. Amer. Math. Soc. 5, (1954). 283--287.

20. Blackwell, David Equivalent comparisons of experiments . Ann. Math. Statistics 24, (1953). 265--272.

19. Blackwell, David On randomization in statistical gameswith $k$ terminal actions . Contributions to the theory of games, vol. 2, pp. 183--187. Annals of Mathematics Studies, no. 28. Princeton University Press, Princeton, N. J., 1953.

18. Arrow, K. J.; Barankin, E. W.; Blackwell, D. Admissible points of convex sets . Contributions to the theory of games, vol. 2, pp. 87--91. Annals of Mathematics Studies, 28. Princeton University Press, Princeton, N. J., 1953.

17. Smith, Nicholas M., Jr.; Walters, Stanley S.; Brooks, Franklin C.; Blackwell, David H. The theory of value and the science of decision, a summary . J. Operations Res. Soc. Amer. 1, (1953). 103--113.

16. Blackwell, David Extension of a renewal theorem . Pacific J. Math. 3, (1953). 315--320.

15. Blackwell, David Comparison of experiments . Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, pp. 93--102. University of California Press, Berkeley and Los Angeles, 1951.

14. Bellman, Richard; Blackwell, David On moment spaces . Ann. of Math. (2) 54, (1951). 272--274.

13. Blackwell, David On the translation parameter problem for discrete variables . Ann. Math. Statistics 22, (1951). 393--399.

12. Blackwell, David The range of certain vector integrals . Proc. Amer. Math. Soc. 2, (1951). 390--395.

11. Blackwell, David On a theorem of Lyapunov . Ann. Math. Statistics 22, (1951). 112--114.

10. Arrow, K. J.; Blackwell, D.; Girshick, M. A. Bayes and minimax solutions of sequential decision problems . Econometrica 17, (1949). 213--244.

9. Bellman, Richard; Blackwell, David Some two-person games involving bluffing . Proc. Nat. Acad. Sci. U. S. A. 35, (1949). 600--605.

8. Blackwell, David A renewal theorem , Duke Math. J. 15, (1948). 145--150.

7. Blackwell, D.; Girshick, M. A. A lower bound for the variance of some unbiased sequential estimates , Ann. Math. Statistics 18, (1947). 277--280.

6. Blackwell, David Conditional expectation and unbiased sequential estimation , Ann. Math. Statistics 18, (1947). 105--110.

5. Blackwell, D.; Girshick, M. A. On functions of sequences of independent chance vectors with applications to the problem of the "random walk" in $k$ dimensions , Ann. Math. Statistics 17, (1946). 310--317.

4. Blackwell, David On an equation of Wald , Ann. Math. Statistics 17, (1946). 84--87.

3. Blackwell, David Finite non-homogeneous chains , Ann. of Math. (2) 46, (1945). 594--599.

2. Blackwell, David The existence of anormal chains , Bull. Amer. Math. Soc. 51, (1945). 465--468.

1. Blackwell, David Idempotent Markoff chains , Ann. of Math. (2) 43, (1942). 560--567.

Also see Our David Blackwell Page1 and Page3 and the SUMMA David Blackwell page; You can reach him through the The David Blackwell Home Page.

References: [DeGroot]; [Donaldson]; [Ferguson]; [Kenschaft-pre]; [Lehman]; [MathReviews]; [Newell]; [vonNeuman]; [ZentralblättReviews].

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