Statistical Science

A Conversation with Ulf Grenander

Nitis Mukhopadhyay

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Ulf Grenander was born in Vastervik, Sweden, on July 23, 1923. He started his undergraduate education at Uppsala University, and earned his B.A. degree in 1946, the Fil. Lic. degree in 1948 and the Fil. Dr. degree in 1950, all from the University of Stockholm. His Ph.D. thesis advisor was Harald Cramér. Professor Grenander is well known for pathbreaking research in a number of areas including pattern theory, computer vision, inference in stochastic processes, probabilities on algebraic structures and actuarial mathematics. He has published more than one dozen influential books, of which Statistical Analysis of Stationary Time Series (1957, coauthored with M. Rosenblatt), Probabilities on Algebraic Structures (1963; also in Russian) and Abstract Inference (1981b) are regarded as classics. His three-volume lecture notes, namely, Pattern Synthesis (vol. I, 1976), Pattern Analysis (vol. II, 1978) and Regular Structures (vol. III, 1981a; also in Russian) created and nurtured a brand new area of research. During 1951–1966, Professor Grenander’s career path took him to the University of Chicago (1951–1952), the University of California–Berkeley (1952–1953), the University of Stockholm (1953–1957), Brown University (1957–1958) and the Institute for Insurance Mathematics and Mathematical Statistics (1958–1966) as its Professor and Director. From 1966 until his retirement he was L. Herbert Ballou University Professor at Brown University. Professor Grenander also held the position of Scientific Director (1971–1973) of the Swedish Institute of Applied Mathematics. He has earned many honors and awards, including Arhennius Fellow (1948), Fellow of the Institute of Mathematical Statistics (1953), Prize of the Nordic Actuaries (1961), Arnberger Prize of the Royal Swedish Academy of Science (1962), Member of the Royal Swedish Academy of Science (1965), Guggenheim Fellowship (1979) and Honorary Fellow of the Royal Statistical Society, London (1989). He has delivered numerous prestigious lectures, including the Rietz Lecture (1985), the Wald Lectures (1995) and the Mahalanobis Lecture (2004). Professor Grenander received an Honorary D.Sc. degree (1993) from the University of Chicago and is a Fellow of both the American Academy of Arts and Sciences (1995) and the National Academy of Sciences, U.S.A. (1998). Professor Grenander’s career, life, passion and hobbies can all be summarized by one simple word: Mathematics.

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Statist. Sci., Volume 21, Number 3 (2006), 404-426.

First available in Project Euclid: 20 December 2006

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Mukhopadhyay, Nitis. A Conversation with Ulf Grenander. Statist. Sci. 21 (2006), no. 3, 404--426. doi:10.1214/088342305000000313.

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  • Cramér, H. (1946). Mathematical Methods of Statistics. Princeton Univ. Press.
  • Dalenius, T. (1950). The problem of optimum stratification. Skand. Aktuarietidskrift 33 203--213.
  • Dalenius, T. and Hodges, J. L. (1957). The choice of stratification points. Skand. Aktuarietidskrift 40 198--203.
  • Dalenius, T. and Hodges, J. L. (1959). Minimum variance stratification. J. Amer. Statist. Assoc. 54 88--101.
  • Grenander, U. (1950). Stochastic processes and statistical inference. Ark. Mat. 1 195--277. (Ph.D. thesis, Univ. Stockholm. Also available as a monograph in Russian, Hungarian and Chinese.)
  • Grenander, U. (1956). On the theory of mortality measurement. I. Skand. Aktuarietidskrift 39 70--96.
  • Grenander, U. (1957). On the theory of mortality measurement. II. Skand. Aktuarietidskrift 39 125--153.
  • Grenander, U. (1958). Some remarks on bonus systems in automobile insurance. Skand. Aktuarietidskrift 40 180--197.
  • Grenander, U. (1963). Probabilities on Algebraic Structures. Wiley, New York. (Also available in Russian.)
  • Grenander, U. (1976). Pattern Synthesis: Lectures in Pattern Theory 1. Springer, New York.
  • Grenander, U. (1978). Pattern Analysis: Lectures in Pattern Theory 2. Springer, New York.
  • Grenander, U. (1981a). Regular Structures: Lectures in Pattern Theory 3. Springer, New York. (Also available in Russian.)
  • Grenander, U. (1981b). Abstract Inference. Wiley, New York.
  • Grenander, U. (1982). Mathematical Experiments on the Computer. Academic Press, New York.
  • Grenander, U. (1993). General Pattern Theory. Oxford Univ. Press.
  • Grenander, U. (1996). Elements of Pattern Theory. Johns Hopkins Univ. Press, Baltimore.
  • Grenander, U., Chow, Y. and Keenan, D. M. (1991). HANDS: A Pattern-Theoretic Study of Biological Shapes. Springer, New York.
  • Grenander, U. and Miller, M. I. (1994). Representations of knowledge in complex systems (with discussion). J. Roy. Statist. Soc. Ser. B 56 549--603.
  • Grenander, U. and Miller, M. I. (2005). Pattern Theory: From Representation to Inference. Oxford University Press, New York. To appear.
  • Grenander, U. and Rosenblatt, M. (1957). Statistical Analysis of Stationary Time Series. Wiley, New York. [2nd ed. (1984), Chelsea, New York.],
  • Grenander, U. and Sethuraman, J. (1994). Mixed limit theorems for pattern analysis. J. Multivariate Anal. 51 414--431.
  • Grenander, U. and Szegö, G. (1958). Toeplitz Forms and Their Applications. Univ. California Press, Berkeley. [2nd ed. (1984), Chelsea, New York.] (Also available in Russian.), ()
  • Hǎjek, J. (1964). Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann. Math. Statist. 35 1491--1523.
  • Kurien, T. V. and Sethuraman, J. (1993a). A mixed limit theorem for stable random fields. J. Multivariate Anal. 47 152--162.
  • Kurien, T. V. and Sethuraman, J. (1993b). Singularities in Gaussian random fields. J. Theoret. Probab. 6 89--99.
  • Rao, M. M. (2000). Stochastic Processes: Inference Theory. Kluwer, Dordrecht.