Ulf Grenander - Misplaced Pages

Swedish American mathematician

Ulf Grenander

Born	(1923-07-23)23 July 1923 Västervik, Sweden
Died	12 May 2016(2016-05-12) (aged 92) Providence, Rhode Island, US
Nationality	Swedish
Alma mater	Stockholm University Uppsala University
Known for	Sieve estimation Pattern theory Maximum subarray problem Computational anatomy
Awards	Royal Swedish Academy of Sciences National Academy of Sciences
Scientific career
Fields	Statistics Mathematics Computer science
Institutions	Stockholm University Brown University
Doctoral advisor	Harald Cramér
Doctoral students	Sven Erlander
Other notable students	Per Martin-Löf

Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish statistician and professor of applied mathematics at Brown University.

His early research was in probability theory, stochastic processes, time series analysis, and statistical theory (particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator). In recent decades, Grenander contributed to computational statistics, image processing, pattern recognition, and artificial intelligence. He coined the term pattern theory to distinguish from pattern recognition.

Honors

In 1966 Grenander was elected to the Royal Academy of Sciences of Sweden, and in 1996 to the US National Academy of Sciences. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He received an honorary doctorate in 1994 from the University of Chicago, and in 2005 from the Royal Institute of Technology of Stockholm, Sweden.

Education

Grenander earned his undergraduate degree at Uppsala University. He earned his Ph.D. at Stockholm University in 1950 under the supervision of Harald Cramér.

Appointments

He was active as a 1950–1951 Associate Professor at Stockholm University, 1951–1952 at University of Chicago, At 1952–1953 University of California–Berkeley, At Stockholm University 1953–1957, at Brown University 1957–1958 and 1958–1966 again at Stockholm University, where he succeeded in 1959 Harald Cramér as the Professor in actuarial science and mathematical statistics. From 1966 until his retirement, Grenander was L. Herbert Ballou University Professor at Brown University. In 1969–1974 he was also professor of Applied Mathematics at The Royal Institute of Technology.

Selected works

Grenander, Ulf (2012). A Calculus of Ideas: A Mathematical Study of Human Thought. World Scientific Publishing. ISBN 978-9814383189.
Grenander, Ulf; Miller, Michael (2007). Pattern Theory: From Representation to Inference. Oxford University Press. ISBN 978-0199297061.
Grenander, Ulf (1996). Elements of Pattern Theory. Johns Hopkins University Press. ISBN 978-0801851889.
Grenander, Ulf (1994). General Pattern Theory. Oxford Science Publications. ISBN 978-0198536710.
Grenander, Ulf (1982). Mathematical Experiments on the Computer. Academic Press. ISBN 9780123017505.
Grenander, Ulf (1981). Abstract Inference. Wiley. ISBN 978-0471082675.
Grenander, Ulf (1963). Probabilities on Algebraic Structures. Wiley.
Grenander, Ulf (1959). Probability and Statistics: The Harald Cramér Volume. Wiley.
Szegő, Gábor; Grenander, Ulf (1958). Toeplitz forms and their applications. Chelsea.
Grenander, Ulf; Rosenblatt, M (1957). Statistical Analysis of Stationary Time Series. American Mathematical Society. ISBN 978-0-8284-0320-7.

Notes

Ulf Grenander Obituary - Providence, RI | The Providence Journal, accessed 28 May 2016
Bentley, Jon (1984). "Programming pearls: algorithm design techniques". Communications of the ACM. 27 (9): 865–873. doi:10.1145/358234.381162. S2CID 207565329..
Mumford, David; Desolneux, Agnès (2010). Pattern Theory: The Stochastic Analysis of Real-World Signals. A K Peters/CRC Press. p. 1. ISBN 978-1568815794. The term "pattern theory" was coined by Ulf Grenander to distinguish his approach to the analysis of patterned structures in the world from "pattern recognition."
Grenander, Ulf (1998). "Strategies for seeing". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III. pp. 585–592.
KTH: Hedersdoktorer 1944–2008 Archived 2010-03-24 at the Wayback Machine, accessed 5 April 2009
Mukhopadhyay, Nitis (2006). "A conversation with Ulf Grenander". Statistical Science. 21 (3): 404–426. arXiv:math/0701092. Bibcode:2007math......1092M. doi:10.1214/088342305000000313. S2CID 62516244.
Grenander, Ulf (1950). Stochastic processes and statistical inference. Arkiv för matematik, 0004-2080; 1:17 (in Swedish). Stockholm: Almqvist & Wiksell.
KTH: En kort historik över professorer vid Institutionen för Matematik, accessed 1 maj 2010
Perlis, Alan J. (1985). "Review: Mathematical experiments on the computer by Ulf Grenander" (PDF). Bull. Amer. Math. Soc. (N.S.). 12 (1): 143–145. doi:10.1090/s0273-0979-1985-15322-4.
Furstenberg, Harry (1965). "Review: Probabilities on algebraic structures bu Ulf Grenander" (PDF). Bull. Amer. Math. Soc. 71 (1): 132–135. doi:10.1090/s0002-9904-1965-11249-6.
Spitzer, F. (1959). "Review: Toeplitz Forms and Their Applications by Ulf Grenander and Gabor Szegő". Bull. Amer. Math. Soc. 65 (2): 97–101. doi:10.1090/s0002-9904-1959-10296-2.
Darling, Donald A. (1958). "Review: Statistical analysis of stationary time series by Ulf Grenander and Murray Rosenblatt" (PDF). Bull. Amer. Math. Soc. 64 (2): 70–71. doi:10.1090/s0002-9904-1958-10172-x.

References

Mukhopadhyay, Nitis (2006). "A conversation with Ulf Grenander". Statistical Science. 21 (3): 404–426. arXiv:math/0701092. Bibcode:2007math......1092M. doi:10.1214/088342305000000313. ISSN 0883-4237. MR 2339138. S2CID 62516244.

External links

Statistics

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in
Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons
Parametric tests	Likelihood-ratio Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC
Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis	Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)
Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression
Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Homoscedasticity and Heteroscedasticity
Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality
Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey
Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)
Frequency domain	Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time
Hazard function	Nelson–Aalen estimator
Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

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