Ulf Grenander Research Articles

A tribute to Ulf Grenander

A tribute to Ulf Grenander

Spatial statistics: Marks, maps, and shapes

ABSTRACTSpatial statistics is concerned with phenomena unfolding in space and possibly also evolving in time, expressing a system of interactions whereby an observation made at a (spatiotemporal) location is informative about observations made at other locations. In general, the interactions are best described probabilistically, rather than deterministically. Spatial scales range from the microscopic (for example, when describing interactions between molecules of a liquid) to planetary (for example, when studying the Earth’s ozone layer) or even larger; temporal scales are similarly varied.Marks indicate objects whose spatial locations are influenced by the presence and nature of other objects nearby: trees of the same or different species in a grove, molecules in a liquid, or galaxies throughout the universe. The statistical models are (marked) spatial point processes.Maps describe the variability of the values of a property across a geographical region. The Ising model of ferromagnetism describes collective properties of atoms arranged in a regular lattice. When mapping the prevalence or the incidence of a disease at the level of counties or parishes, the observations are associated with subsets of a region whose spatial relations are meaningful. Many maps are drawn based on observations made at a finite set of locations distributed either regularly or irregularly throughout a 2D or 3D spatial domain. For example, the mass fraction of uranium in soils and surface sediments across Colorado. Gaussian random functions are a model of choice for such quantities, possibly after re-expression.Shapes arise owing to modulated interactions between surface elements anchored to points in space — “generators” in the nomenclature of Ulf Grenander’s pattern theory. Probability distributions on spaces of generators and on spaces of interactions between them can then be used to describe variations on patterns and to fit shape models.

Philippe G. Schyns

Philippe G. Schyns

Pattern Theory: from Recognition to Inference by Ulf Grenander and Michael Miller

Pattern Theory: from Recognition to Inference by Ulf Grenander and Michael Miller

Book Review: Ulf Grenander and Michael Miller, Pattern Theory. From representation to inference.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 87, Issue 7 p. 527-527 Book Review Book Review: Ulf Grenander and Michael Miller, Pattern Theory. From representation to inference. Dirk Lorenz, Dirk Lorenz Bremen, GermanySearch for more papers by this author Dirk Lorenz, Dirk Lorenz Bremen, GermanySearch for more papers by this author First published: 18 July 2007 https://doi.org/10.1002/zamm.200790015AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume87, Issue7July 2007Pages 527-527 RelatedInformation

A Conversation with Ulf Grenander

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.

Spatial Statistics and Bayesian Computation

SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of MCMC in general Bayesian computation. In this paper, we trace the early development of MCMC in Bayesian inference, review some recent computational progress in statistical physics, based on the introduction of auxiliary variables, and discuss its current and future relevance in Bayesian applications. We briefly describe a simple MCMC implementation for the Bayesian analysis of agricultural field experiments, with which we have some practical experience.

Elliptic Law

Elliptic Law

A sieve method for the spectral density : Yun-Shyong Chow, ∗Institute of Mathematics, Academia Sinica, Taipei, Taiwan, China Ulf Grenander, Brown University, Providence, RI, USA

A sieve method for the spectral density : Yun-Shyong Chow, ∗Institute of Mathematics, Academia Sinica, Taipei, Taiwan, China Ulf Grenander, Brown University, Providence, RI, USA

On the Decomposition of Gaussian Distributions on Groups

Previous article Next article On the Decomposition of Gaussian Distributions on GroupsG. M. Fel’dmanG. M. Fel’dmanhttps://doi.org/10.1137/1122012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Linnik and , I. V. Ostrovskii, Decomposition of random variables and random vectors, Nauka, Moscow, 1972, (English translation: AMS translations of mathematical monographs No. 48, 1977) Google Scholar[2] J. Marcinkiewicz, Sur les variables aléatoires enroulées, C.R. Séances et Conf. Soc. Math. de France, 1938 (1939), 34–36 0024.26403 Google Scholar[3] Ulf Grenander, Probabilities on algebraic structures, John Wiley & Sons Inc., New York, 1963, 218– MR0206994 0131.34804 Google Scholar[4] K. R. Parthasarathy, , R. Ranga Rao and , S. R. S. Varadhan, Probability distributions on locally compact abelian groups, Illinois J. Math., 7 (1963), 337–369 MR0190968 0129.10902 CrossrefGoogle Scholar[5] V. V. Sazonov and , V. N. Tutubalin, Probability distributions on topological groups, Theory Prob. Applications, 11 (1966), 1–45 10.1137/1111001 0171.38701 LinkGoogle Scholar[6] L. S. Pontriyagin, Continuous Groups, Nauka, Moscow, 1973 Google Scholar[7] A. Weil, Integration on topological groups and its application, Actualités Sci. et Ind. 69, Hermann, Paris, 1940 Google Scholar[8] K. Urbanik, Guassian measures on locally compact Abelian topological groups, Studia Math., 19 (1960), 77–88 MR0112916 0099.01704 CrossrefGoogle Scholar[9] V. M. Zolotarev, General theory of the multiplication of random variables, Dokl. Akad. Nauk SSSR, 142 (1962), 788–791 MR0132562 Google Scholar[10] A. P. Robertson and , W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, New York, 1964viii+158 MR0162118 0123.30202 Google Scholar[11] Herbert Heyer, Factorization of probability measures on locally compact groups, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 231–258 10.1007/BF00531525 MR0219100 0153.19302 CrossrefGoogle Scholar[12A] Nicolas Bourbaki, Elements of mathematics. General topology. Part 1, Hermann, Paris, 1966vii+437 MR0205210 0301.54001 Google Scholar[12B] Nicolas Bourbaki, Elements of mathematics. General topology. Part 2, Hermann, Paris, 1966iv+363 MR0205211 0301.54002 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Characterization of distributions of Q -independent random variables on locally compact Abelian groupsStatistics & Probability Letters, Vol. 152 Cross Ref $p$-Адические гауссовские случайные величины9 December 2019 | Труды Математического института имени В.А. Стеклова, Vol. 306 Cross Ref p-Adic Gaussian Random Variables28 December 2019 | Proceedings of the Steklov Institute of Mathematics, Vol. 306, No. 1 Cross Ref On notions of Q-independence and Q-identical distributivenessStatistics & Probability Letters, Vol. 140 Cross Ref Heyde's Characterization Theorem for Some Locally Compact Abelian GroupsG. M. Feldman8 August 2018 | Theory of Probability & Its Applications, Vol. 62, No. 3AbstractPDF (218 KB)Characterization theorems for Q-independent random variables with values in a locally compact Abelian group3 May 2017 | Aequationes mathematicae, Vol. 91, No. 5 Cross Ref On the Heyde theorem for some locally compact Abelian groups17 May 2017 | Doklady Mathematics, Vol. 95, No. 2 Cross Ref Характеризационная теорема Хейде на некоторых локально компактных абелевых группахТеория вероятностей и ее применения, Vol. 62, No. 3 Cross Ref Independent Linear Statistics on the Cylinders9 June 2015 | Theory of Probability & Its Applications, Vol. 59, No. 2AbstractPDF (263 KB)Independent Linear Statistics on $\mathbfa$-Adic Solenoids26 August 2010 | Theory of Probability & Its Applications, Vol. 54, No. 3AbstractPDF (227 KB)On a characterization theorem for locally compact abelian groups15 March 2005 | Probability Theory and Related Fields, Vol. 133, No. 3 Cross Ref L Cross Ref On the Skitovich–Darmois Theorem on Abelian Groups17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 4AbstractPDF (1212 KB)Marcinkiewicz and Lukacs Theorems on Abelian Groups17 July 2006 | Theory of Probability & Its Applications, Vol. 34, No. 2AbstractPDF (912 KB)L Cross Ref On a Characterization of the Gaussian Distribution on Abelian Groups17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 3AbstractPDF (558 KB)Bernstein Gaussian Distributions on Groups1 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 1AbstractPDF (1193 KB)The Arithmetic of Probability Distributions1 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 1AbstractPDF (3141 KB)On Infinitely Divisible Distributions of the Class $I_0 $ on Groups17 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 3AbstractPDF (1252 KB)On the decomposition of the convolution of a Gaussian and poisson distribution on locally compact Abelian groupsJournal of Multivariate Analysis, Vol. 13, No. 1 Cross Ref Decomposition of the Convolution of Two Poisson Distributions on a Locally Compact Abelian Group17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 3AbstractPDF (668 KB)Decomposition of probability measures on locally compact abelian groups22 October 2006 Cross Ref Gaussian Distributions on Locally Compact Abelian Groups17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 3AbstractPDF (1385 KB) Volume 22, Issue 1| 1977Theory of Probability & Its Applications History Submitted:30 September 1975Published online:17 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1122012Article page range:pp. 133-140ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Book Reviews

Abstract Statistical Methods in Research and Production; Owen L. Davies and Peter L. Goldsmith (Editors). New York: Hafner Publishing Co., Inc., 1972. xiii + 478 pp., $16.00. Reviewed by John Mandel Pattern Classification and Scene Analysis; Richard O. Duda and Peter E. Hart. New York: John Wiley and Sons, Inc., 1973. xvii + 482 pp. $22.50. Reviewed by Ulf Grenander Applied Time Series Analysis for Managerial Forecasting; Charles R. Nelson. San Francisco: Holden-Day, Inc., 1973. xiv + 231 pp. $13.95. Reviewed by D. M. Dunn A Consumption-Savings Model and Its Applications; W. H. Somermeyer and R. Bannink. New York: American Elsevier Publishing Company, Inc., 1973. xvi + 431 pp. $34.75. Reviewed by Lester D. Taylor Monte Carlo Methods: Their Role for Econometrics; V. Kerry Smith. Lexington, Massachusetts: Lexington Books, 1973. xiv + 153 pp. $15.00. Reviewed by Roy F. Gilbert Distribution Theory for Tests Based on the Sample Distribution Function; J. Durbin. Philadelphia: Society for Industrial and Applied Mathematics, 1973. vi + 64 pp. $4.80 paperback. Reviewed by Philip Holgate Statistics and Society: Data Collection and Interpretation; Walter T. Federer. New York: Marcel Dekker, Inc., 1973. ix + 399 pp. $14.50. Reviewed by James W. Yackel Structural Equation Models in the Social Sciences; Arthur S. Goldberger and Otis Dudley Duncan (Editors). New York: Seminar Press Inc., 1973. xv + 358 pp. $15.95. Reviewed by Lester D. Taylor Standard Statistical Calculations, 2nd Edition; P.G. Moore, E.A. Shirley and D.E. Edwards (Editors). New York: John Wiley and Sons, Inc., 1973. xi + 123 pp. $6.75. Reviewed by R. Dennis Cook Econometric Studies of Macro and Monetary Relations; Alan A. Powell and Ross A. Williams (Editors). New York: American Elsevier Publishing Company, Inc., 1973. viii + 358 pp. $20.00. Reviewed by Michael D. Hurd Spatial Autocorrelation; A.D. Cliff and J.K. Ord. London: Pion Limited, 1973. 178 pp. 2.50. Reviewed by Alexander Lebanon Multivariate Statistical Methods for Business and Economics; Ben W. Bolch and Cliff J. Huang. Englewood Cliffs: Prentice-Hall, 1974, xiv + 329 pp. $12.95. Reviewed by J. Kmenta Brief Reviews: Econometric Estimation; J.C.R. Rowley. New York: John Wiley and Sons, 1973. ix + 234 pp. $14.50 Brief Reviews: Symmetric Functions in Statistics: Proceedings of a Symposium in Honor of Professor Paul S. Dwyer; Derrick S. Tracy (ed.). Windsor, Ontario: University of Windsor, 1972. 224 pp. $4.50 paperback Brief Reviews: 5th Conference on Optimization Techniques; R. Conti and A. Ruberti (eds.). New York: Springer-Verlag, 1973. Part I, xiii + 565 pp. $14.70, paperback. Part II, xiii + 389 pp. $10.80, paperback Brief Reviews: Inventory Control and Water Storage; A. Prékopa (ed.). New York: American Elsevier Publishing Company, Inc., 1974. 382 pp. $28.00 Brief Reviews: Symposium on the Theory of Scheduling and Its Applications; S.E. Elmaghraby (ed.). New York: Springer-Verlag, 1974. viii + 437 pp. $13.20 paperback

$L_p $-Criteria for the Estimation of Location Parameters

$L_p $-Criteria for the Estimation of Location Parameters

Book Reviews

Abstract Abstract Monte Carlo Methods. J. M. Hammersley and D. C. Handscomb. (Methuen's Monographs on Applied Probability and Statistics.) New York: John Wiley and Sons, Inc., 1964. Pp. vii, 178. $4.75. Reviewed by Martin Greenberger Studies in Subjective Probability. Henry E. Kyburg, Jr. and Howard E. Smokler, Editors. New York: John Wiley and Sons, Inc., 1964. Pp. vii, 203. $4.75. Paperbound. Reviewed by Bruce M. Hill Probabilities on Algebraic Structures. Ulf Grenander. New York: John Wiley and Sons, Inc., 1963. Pp. 218. $12.00. Reviewed by G. Kallianpur The Method of Paired Comparisons. H. A. David, New York: Hafner Publishing Company, 1963. Pp. 124. $4.75. Reviewed by Gottfried E. Noether Investment Decisions, Economic Forecasting, and Public Policy. John R. Meyer and Robert R. Glauber. Boston, Massachusetts: Harvard University Graduate School of Business Administration, 1964. Pp. xix, 280. $6.00. Reviewed by James W. Friedman 1963 Survey of Consumer Finances. George Katona, Charles A. Lininger, and Eva Mueller. Ann Arbor, Michigan: University of Michigan Survey Research Center, 1964. Pp. xviii, 259. $6.00. Reviewed by James C. Byrnes Basic Statistics: A Primer for the Biomedical Sciences. Olive Jean Dunn. New York: John Wiley and Sons, Inc., 1964. Pp. xiii, 184. $5.50. Reviewed by Richard D. Remington Estimates of Residential Building, United States, 1840–1939. Manuel Gottlieb. (Technical Paper 17.) New York: National Bureau of Economic Research, 1964. Pp. xvi, 99. $2.00. Paperbound. Reviewed by Dorothy S. Brady Housing Market Analysis and the Growth of Nonfarm Home Ownership. Alvin E. Coons and Bert T. Glaze. (Bureau of Business Research Monograph Number 115.) Columbus, Ohio: Bureau of Business Research, Ohio State University, 1963. Pp. xix, 174. $5.00. Reviewed by Hugh O. Nourse The Behavior of Income Shares: Selected Theoretical and Empirical Issues. National Bureau of Economic Research, Inc. Princeton, New Jersey: Princeton University Press for the National Bureau of Economic Research, Inc., 1964. Pp. x, 394. $8.00. Reviewed by Harold M. Somers A Behavioral Theory of the Firm. Richard M. Cyert and James G. March. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1963. Pp. ix, 332. $8.25. Reviewed by Martin Shubik Planning and Statistics in Socialist Countries. I. Y. Pisarev, et al. (Indian Statistical Series No. 19.) New York: Taplinger Publishing Company, Inc., for the Asia Publishing House, 1964. Pp. vi, 256. $13.00. Reviewed by Egon Neuberger The Random Character of Stock Market Prices. Paul H. Cootner, Editor. Cambridge, Massachusetts: Massachusetts Institute of Technology Press, 1964. Pp. ix, 510. $15.00. Reviewed by Harry Markowitz Skid Row in American Cities. Donald J. Bogue. Chicago, Illinois: Community and Family Study Center, University of Chicago, 1964. Pp. xiv, 521. $6.50. Reviewed by Mary G. Powers Adaptive Control Processes: A Guided Tour. Richard Bellman. Princeton, New Jersey: Princeton University Press, 1961. Pp. xvi, 255. $6.50. Reviewed by Marshall Freimer Electronic Computation of Human Diets. Victor E. Smith. East Lansing: Michigan State University Graduate School of Business Administration, 1964. Pp. xvii, 234, $8.00. Reviewed by Walter D. Fisher Introduction To Experimental Statistics. C. C. Li. New York: McGraw-Hill Book Company, 1964. Pp. x, 460. $11.50. Reviewed by Clyde Y. Kramer What Do Statistics Show? F. R. Oliver. London, England: Hodder and Stoughton, Limited, 1964. Pp. 157. 21s. Reviewed by T. A. Bancroft Introduction to the Use of Mathematics in Economic Analysis. David S. Huang. New York: John Wiley and Sons, Inc., 1964. Pp. xvi, 281. $6.95. Reviewed by James Quirk Essential Methods in Business Statistics. Edward N. Dubois. New York: McGraw-Hill Book Company, 1964. Pp. xiv, 238. $6.95 Reviewed by Max Astrachan

Review: Ulf Grenander, Probabilities on Algebraic Structures

Review: Ulf Grenander, Probabilities on Algebraic Structures

Some Properties of Estimators of the Spectrum of a Stationary Process

Previous article Next article Some Properties of Estimators of the Spectrum of a Stationary ProcessT. L. MalevichT. L. Malevichhttps://doi.org/10.1137/1110053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov, On estimation of the spectral function of a stationary Gaussian process, Theory Prob. Applications, 8 (1963), 366–401, (English translation.) 10.1137/1108044 0137.12901 LinkGoogle Scholar[2] I. A. Ibragimov, Estimate of the spectrum of a stationary Gaussian process, Dokl. Akad. Nauk SSSR, 141 (1961), 296–299, (In Russian.) MR0131950 Google Scholar[3] Ulf Grenander and , Murray Rosenblatt, Statistical analysis of stationary time series, John Wiley & Sons, New York, 1957, 300– MR0084975 0080.12904 Google Scholar[4] Ulf Grenander and , Murray Rosenblatt, Some problems in estimating the spectrum of a time series, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. I, University of California Press, Berkeley and Los Angeles, 1956, 77–93 MR0084914 0072.36401 Google Scholar[5] T. L. Malevich, The asymptotic behavior of an estimate for the spectral function of a stationary Gaussian process, Theory Prob. Applications, 9 (1964), 350–353, (English translation.) 10.1137/1109052 0132.38401 LinkGoogle Scholar[6] I. A. Ibragimov and , T. M. Tovstik, An estimate for spectral functions of a class of stationary random sequences, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom., 19 (1964), 42–57, (In Russian.) MR0165585 Google Scholar[7] S. N. Bernshtein, Probability Theory, Gostekhizdat, Moskva, 1946, (In Russian.) Google Scholar[9] G. M. Fikhtengol'ts, Course on Differential and Integral Calculus, Vol. III, Gostekhizdat, Moskva, 1949, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Asymptotic properties of spectral estimates of second order9 November 2011 Cross Ref On the Uniform Convergence of Estimates of the Spectral Density of a Stationary Gaussian Random ProcessV. G. Alekseev28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 1AbstractPDF (608 KB)Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian ProcessT. L. Malevich17 July 2006 | Theory of Probability & Its Applications, Vol. 14, No. 2AbstractPDF (630 KB) Volume 10, Issue 3| 1965Theory of Probability & Its Applications History Submitted:14 April 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110053Article page range:pp. 457-465ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Absolute Continuity of Infinitely Divisible Distributions under Translations

Previous article Next article Absolute Continuity of Infinitely Divisible Distributions under TranslationsA. V. SkorokhodA. V. Skorokhodhttps://doi.org/10.1137/1110054PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Ulf Grenander, Stochastic processes and statistical inference, Ark. Mat., 1 (1950), 195–277 MR0039202 0058.35501 CrossrefGoogle Scholar[2] Emanuel Parzen, Regression analysis of continuous parameter time seriesProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, Univ. California Press, Berkeley, Calif., 1961, 469–489 MR0146931 0107.13802 Google Scholar[3] A. V. Skorokhod, Random Processes with Independent Increments, Izd-vo “Nauka”, Moskva, 1964, (In Russian.) Google Scholar[4] T. S. Pitcher, The admissible mean values of a stochastic process, Trans. Amer. Math. Soc., 108 (1963), 538–546 MR0171311 0122.36303 CrossrefGoogle Scholar[5] A. V. Skorokhod, On the differentiability of measures which correspond to stochastic processes. I. Processes with independent increments, Theory Prob. Applications, 2 (1957), 407–432, (English translation.) 10.1137/1102030 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the structure of monoids of admissible transplates of multivariate probability measuresSemigroup Forum, Vol. 27, No. 1 Cross Ref A conditional dichotomy theorem for stochastic processes with independent incrementsJournal of Multivariate Analysis, Vol. 7, No. 1 Cross Ref Admissible transformations of measuresSemigroup Forum, Vol. 12, No. 1 Cross Ref The Structure of Infinitely Divisible Distributions on a Bicompact Abelian GroupV. M. Zolotarev and V. M. Kruglov17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 4AbstractPDF (1213 KB)Densities for infinitely divisible random processesJournal of Multivariate Analysis, Vol. 5, No. 2 Cross Ref On Admissible Translations of Measures in Hilbert SpaceA. V. Skorokhod17 July 2006 | Theory of Probability & Its Applications, Vol. 15, No. 4AbstractPDF (1636 KB) Volume 10, Issue 3| 1965Theory of Probability & Its Applications History Submitted:14 January 1965Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110054Article page range:pp. 465-472ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

On the Computation of the Likelihood Ratio for Gaussian Processes with a Rational Spectrum

Previous article Next article On the Computation of the Likelihood Ratio for Gaussian Processes with a Rational SpectrumV. F. PisarenkoV. F. Pisarenkohttps://doi.org/10.1137/1110034PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. F. Pisarenko and , Yu. A. Rozanov, On certain problems for stationary processes leading to integral equations related to Wiener-Hopf equations, Problemy Peredači Informacii No., 14 (1963), 113–135, (In Russian.) MR0192564 Google Scholar[2] V. F. Pisarenko, A Wiener-Hopf type equation for higher-dimensional random processes with a rational spectral density, Dokl. Akad. Nauk SSSR, 149 (1963), 776–779, (In Russian.) MR0153056 0131.16305 Google Scholar[3] V. F. Pisarenko, Masters Thesis, Some statistical problems for multi-dimensional processes with a rational spectrum, Candidate's theses, Vil'nyus, 1963, (In Russian.) Google Scholar[4] Jaroslav Hájek, On linear statistical problems in stochastic processes, Czechoslovak Math. J., 12 (87) (1962), 404–444 MR0152090 0114.34504 Google Scholar[5] I. M. Gel'fand and , A. M. Yaglom, Computation of the amount of information about a stochastic function contained in another such function, Uspehi Mat. Nauk (N.S.), 12 (1957), 3–52, (In Russian.) MR0085153 Google Scholar[6] Walter F. Freiberger, An approximate method in signal detection, Quart. Appl. Math., 20 (1962/1963), 373–378 MR0139498 0111.14404 CrossrefGoogle Scholar[7] Ulf Grenander and , Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley, 1958vii+245 MR0094840 0080.09501 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Statistical inference for stationary linear models with tapered dataStatistics Surveys, Vol. 15, No. none Cross Ref Absolute Continuity29 September 2014 Cross Ref Absolute Continuity15 August 2006 Cross Ref On Sufficient Statistics of Gaussian Processes with Rational Spectral Density FunctionM. Arató28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 1AbstractPDF (900 KB)On Parameter Estimation in the Presence of NoiseM. Arató17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 3AbstractPDF (638 KB)Remarks on the Approximation of the Likelihood Function of a Stationary Gaussian ProcessJ. Coursol and D. Dacunha-Castelle17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 1AbstractPDF (428 KB)Tests of Composite Hypotheses for Random Variables and Stochastic ProcessesK. O. Dzhaparidze17 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 1AbstractPDF (1375 KB)On Evaluation of the Likelihood Ratio for a Generalized Gaussian Process with Rational Spectral DensityK. O. Dzaparidze and G. I. Marr28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 2AbstractPDF (357 KB)On the Estimation of the Spectral Parameters of a Gaussian Stationary Process with Rational Spectral DensityK. O. Dzaparidze17 July 2006 | Theory of Probability & Its Applications, Vol. 15, No. 3AbstractPDF (827 KB)Radon-Nikodym derivatives in case of rational spectral densities Cross Ref On the Densities of Gaussian Distributions and Wiener-Hopf Integral EquationsYu. A. Rozanov17 July 2006 | Theory of Probability & Its Applications, Vol. 11, No. 1AbstractPDF (858 KB) Volume 10, Issue 2| 1965Theory of Probability & Its Applications History Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110034Article page range:pp. 299-303ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Probabilities on Algebraic Structures (Ulf Grenander)

Previous article Next article Probabilities on Algebraic Structures (Ulf Grenander)Meyer DwassMeyer Dwasshttps://doi.org/10.1137/1006086PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Probabilities on Algebraic Structures (Ulf Grenander)." SIAM Review, 6(3), pp. 323–324 Previous article Next article FiguresRelatedReferencesCited byDetails Volume 6, Issue 3| 1964SIAM Review History Published online:18 July 2006 InformationCopyright © 1964 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1006086Article page range:pp. 323-324ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Probability and statistics, edited by Ulf Grenander, John Wiley and Sons, New York, 1959, 434 pp

Probability and statistics, edited by Ulf Grenander, John Wiley and Sons, New York, 1959, 434 pp

Book Reviews

Book Reviews —Sampling Inspection Tables, Second Edition. Harold F. Dodge and Harry G. Romig, New York: John Wiley and Sons, Inc., June 3, 1959: pp. 224. $8.00—reviewed by S. B. L.; —Engineering and Organization, by Everett Laitala. Homewood, Illinois: Richard D. Irwin, Inc., 1959—reviewed by Edward H. Bowman; —Scientific Programming in Business and Industry. By Andrew Vazsonyi. New York: John Wiley & Sons, Inc., 1958—reviewed by Martin K. Starr; —Introduction to Probability and Statistics. By B. W. Lindgren and G. W. McElrath. New York: Macmillan, 1959. xiii plus 277 pages. Price $6.25—reviewed by Harold Freeman; —Mathematical Programming and Electrical Networks by Jack B. Dennis, published jointly by the Technology Press of the Massachusetts Institute of Technology and John Wiley & Sons, Inc., New York, 1959, pp. 186—reviewed by David H. Evans; —Statistical Analysis of Stationary Time Series, by Ulf Grenander and Murray Rosenblatt, New York: John Wiley and Sons, Inc.; 1957; $11.00—reviewed by Simeon N. Berman. Books Received