The 2005 Neyman Lecture: Dynamic Indeterminism in Science
David R. Brillinger
Source: Statist. Sci. Volume 23, Number 1 (2008), 48-64.
Abstract
Jerzy Neyman’s life history and some of his contributions to applied statistics are reviewed. In a 1960 article he wrote: “Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research which, if treated realistically, does not involve operations on stochastic processes. The time has arrived for the theory of stochastic processes to become an item of usual equipment of every applied statistician.” The emphasis in this article is on stochastic processes and on stochastic process data analysis. A number of data sets and corresponding substantive questions are addressed. The data sets concern sardine depletion, blowfly dynamics, weather modification, elk movement and seal journeying. Three of the examples are from Neyman’s work and four from the author’s joint work with collaborators.
Keywords: Animal motion; ATV motion; elk; Jerzy Neyman; lifetable; monk seal; population dynamics; sardines; stochastic differential equations; sheep blowflies; simulation; synthetic data; time series; weather modification
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ss/1215441282
Digital Object Identifier: doi:10.1214/07-STS246
References
Billard, L. and Ferber, M. A. (1991). Elizabeth Scott: Scholar, teacher, administrator. Statist. Sci. 6 206–216.
Mathematical Reviews (MathSciNet):
MR1127863
Digital Object Identifier: doi:10.1214/ss/1177011828
Project Euclid: euclid.ss/1177011828
Brillinger, D. R. (1981). Some aspects of modern population mathematics. Canad. J. Statist. 9 173–194.
Mathematical Reviews (MathSciNet):
MR640015
Digital Object Identifier: doi:10.2307/3314611
JSTOR: links.jstor.org
Brillinger, D. R. (1983). Statistical inference for random processes. In Proceedings of the International Congress of Mathematicians 1, 2 1049–1061. PWN, Warsaw.
Mathematical Reviews (MathSciNet):
MR804757
Brillinger, D. R. (1995). On a weather modification problem of Professor Neyman. Probab. Math. Statist. 15 115–125.
Brillinger, D. R. (2003). Simulating constrained animal motion using stochastic differential equations. Probability, Statistics and Their Applications. IMS Lecture Notes Monograph Series 41 35–48. IMS, Beachwood, OH.
Mathematical Reviews (MathSciNet):
MR1999413
Zentralblatt MATH:
1042.92042
Digital Object Identifier: doi:10.1214/lnms/1215091656
Brillinger, D. R. (2007a). A potential function approach to the flow of play in soccer. J. Quant. Anal. Sports 3 1–21.
Mathematical Reviews (MathSciNet):
MR2304568
Digital Object Identifier: doi:10.2202/1559-0410.1048
Brillinger, D. R. (2007b). Learning a potential function from a trajectory. Signal Processing Letters 14 867–870.
Brillinger, D. R., Guckenheimer, J., Guttorp, P. and Oster, G. (1980). Empirical modeling of population time series data: the case of age and density dependent vital rates. Lectures Mathematics Life Sciences 13 65–90.
Brillinger, D. R., Preisler, H. K., Ager, A. A. and Kie, J. (2001a). The use of potential functions in modelling animal movement. In Data Analysis from Statistical Foundations 369–386. Nova Science, Hutington.
Mathematical Reviews (MathSciNet):
MR2034526
Brillinger, D. R., Preisler, H. K., Ager, A. A., Kie, J. and Stewart, B. S. (2001b). Modelling movements of free-ranging animals. Technical Report 610, UCB Statistics.
Brillinger, D. R., Preisler, H. K., Ager, A. A. and Wisdom, M. J. (2004). Stochastic differential equations in the analysis of wildlife motion. In 2004 Proceedings of the American Statistical Association, Statistics and the Environment Section.
Brillinger, D. R., Stewart, B. S. and Littnan, C. L. (2006). A meandering hylje. In Festschrift for Tarmo Pukkila 79–92. Univ. Tampere, Finland.
Mathematical Reviews (MathSciNet):
MR2412952
Brillinger, D. R., Stewart, B. S. and Littnan, C. L. (2008). Three months journeying of a Hawaiian monk seal. IMS Collections. Probability and Statistics: Essays in Honor of David A. Freedman 2 246–264. IMS, Beachwood, OH.
Dawkins, S., Neyman, J. and Scott, E. L. (1977). The Grossversuch Project. Transactions of Workshop on Total-Area Effects of Weather Modification. Fort Collins, Colorado.
Fix, E. and Neyman, J. (1951). A simple stochastic model of recovery, relapse, death and loss of patients. Human Biology 23 205–241.
Guckenheimer, J. and Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York.
Mathematical Reviews (MathSciNet):
MR709768
Zentralblatt MATH:
0515.34001
Guttorp, P. M. (1980). Statistical modelling of population processes. Ph.D. thesis, Univ. California, Berkeley.
Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.
Mathematical Reviews (MathSciNet):
MR1082147
Zentralblatt MATH:
0747.62061
Heyde, C. (1994). A quasi-likelihood approach to estimating parameters in diffusion type processes. J. Applied Probab. 31A 283–290.
Mathematical Reviews (MathSciNet):
MR1274731
Digital Object Identifier: doi:10.2307/3214962
JSTOR: links.jstor.org
Ito, K. (1951). On stochastic differential equations. Mem. Amer. Math. Soc. 1951 1–51.
Mathematical Reviews (MathSciNet):
MR40618
Kendall, D. G., Bartlett, M. S. and Page, T. L. (1982). Jerzy Neyman, 1894–1981. Biog. Memoirs Fellows Royal Society 28 379–412.
Kloeden, P. E. and Platen, E. (1995). Numerical Solution of Differential Equations. Springer, Berlin.
Le Cam, L. (1995). Neyman and stochastic models. Probab. Math. Statist. 15 37–45.
Mathematical Reviews (MathSciNet):
MR1369790
Le Cam, L. and Lehmann, E. (1974). J. Neyman—on the occasion of his 80th birthday. Ann. Statist. 2 vii-xiii.
Mathematical Reviews (MathSciNet):
MR342345
Digital Object Identifier: doi:10.1214/aos/1176342703
Lehmann, E. (1994). Jerzy Neyman. Biographical Memoirs 63 395–420. National Acad. Sci.
Nelson, E. (1967). Dynamical Theories of Brownian Motion, 2nd ed. Princeton Univ. Press.
Mathematical Reviews (MathSciNet):
MR214150
Zentralblatt MATH:
0165.58502
Neyman, J. (1934). On two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. J. Roy. Statist. Soc. 97 558–606.
Neyman, J. (1938a). Contributions to the theory of sampling human populations. J. Amer. Statist. Assoc. 33 101–116.
Neyman, J. (1938b). Lectures and Conferences on Mathematical Statistics and Probability Theory. USDA, Washington.
Neyman, J. (1947). Outline of the statistical treatment of the problem of diagnosis. Public Health Reports 62 1449–1456.
Neyman, J. (1948). Reports on the Sardine Fishery. Research Department, California Council of the Congress of Industrial Organizations.
Neyman, J. (1949). On the problem of estimating the number of schools of fish. Univ. California Publ. Statist. 1 21–36.
Mathematical Reviews (MathSciNet):
MR38046
Neyman, J. (1960). Indeterminism in science and new demands on statisticians. J. Amer. Statist. Assoc. 55 625–639.
Mathematical Reviews (MathSciNet):
MR116393
Digital Object Identifier: doi:10.2307/2281586
JSTOR: links.jstor.org
Neyman, J. (1966). Behavioristic points of view on mathematical statistics. In On Political Economy and Econometrics 445–462. Polish Scientific Publishers, Warsaw.
Neyman, J. (1967). A Selection of Early Statistical Papers of J. Neyman. Univ. California Press.
Mathematical Reviews (MathSciNet):
MR222983
Neyman, J. (1970). A glance at some of my personal experiences in the process of research. In Scientists at Work (T. Dalenius et al., eds.) 148–164. Almqvist and Wiksells, Uppsala.
Mathematical Reviews (MathSciNet):
MR396141
Neyman, J. (1976). Descriptive statistics vs. chance mechanisms and societal problems. In Proc. 9th Int. Biometrics Conf. II 59–68. Boston.
Neyman, J. (1980). Some memorable incidents in probabilistic/statistical studies. In Asymptotic Theory of Statistical Tests and Estimation (I. M. Chakravarti, ed.) 1–32. Academic, New York.
Mathematical Reviews (MathSciNet):
MR571333
Neyman, J. and Scott, E. L. (1956). The distribution of galaxies. Scientific American September 187–200.
Neyman, J. and Scott, E. L. (1959). Stochastic models of population dynamics. Science 130 303–308.
Mathematical Reviews (MathSciNet):
MR107571
Digital Object Identifier: doi:10.1126/science.130.3371.303
Neyman, J. and Scott, E. L. (1965–1966). Planning an experiment with cloud seeding. Proc. Fifth Berkeley Symposium on Math. Statistics and Probab. 327–350. Univ. California Press, Berkeley.
Neyman, J. and Scott, E. L. (1972). Processes of clustering and applications. In Stochastic Point Processes (P. A. W. Lewis, ed.) 646–681. Wiley, New York.
Neyman, J. and Scott, E. L. (1974). Rain stimulation experiments: design and evaluation. In Proc. WMO/IAMAP Sci. Conf. Weather Modification 449–457. WMO, Geneva.
Neyman, J., Scott, E. L. and Shane, C. D. (1953). On the spatial distribution of galaxies a specific model. Astrophys. J. 117 92–133.
Neyman, J., Scott, E. L. and Shane, C. D. (1954). The index of clumpiness of the distribution of images of galaxies. Astrophys. J. Supp. 8 269–294.
Neyman, J., Scott, E. L. and Wells, M. A. (1969). Statistics in meteorology. Rev. Inter. Stat. Inst. 37 119–148.
Nicholson, A. J. (1957). The self-adjustment of populations to change. Cold Spring Harbor Symp. Quant. Biol. 22 153–173.
Pearson, K. (1900). The Grammar of Science. Dent, London.
Zentralblatt MATH:
31.0075.02
Preisler, H. K., Ager, A. A., Johnson, B. K. and Kie, J. G. (2004). Modelling animal movements using stochastic differential equations. Environmetrics 15 643–657.
Reid, C. (1998). Neyman. Springer, New York.
Mathematical Reviews (MathSciNet):
MR1480666
Scott, E. L. (1957). The brightest galaxy in a cluster as a distance indicator. Astron. J. 62 248–265.
Scott, E. L. (1985). Neyman, Jerzy. Encycl. Stat. Sci. 6 214–223.
Scott, E. L., Shane, C. D. and Wirtanen, C. A. (1954). Comparison of the synthetic and actual distribution of galaxies on a photographic plate. Astrophys. J. 119 91–112.
Sørensen, M. (1997). Estimating functions for discretely observed diffusions: A review. IMS Lecture Notes Monograph Series 32 305–325. IMS, Hayward, CA.
Stewart, B. S., Antonelis, G. A., Yochem, P. K. and Baker, J. D. (2006). Foraging biogeography of Hawaiian monk seals in the northwestern Hawaiian Islands. Atoll Research Bulletin 543 131–145.
Taylor, J. R. (2005). Classical Mechanics. Univ. Science, Sausalito.
Zentralblatt MATH:
1075.70002
Wisdom, M. J. ed. (2005). The Starkey Project. Alliance Communications Group, Lawrence Kansas.
