Statistical Science
- Statist. Sci.
- Volume 7, Number 1 (1992), 69-90.
Statistics, Probability and Chaos
Abstract
The study of chaotic behavior has received substantial attention in many disciplines. Although often based on deterministic models, chaos is associated with complex, "random" behavior and forms of unpredictability. Mathematical models and definitions associated with chaos are reviewed. The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, are emphasized. Popular data analytic methods appearing in the literature are discussed. A major goal of this article is to present some indications of how probability modelers and statisticians can contribute to analyses involving chaos.
Article information
Source
Statist. Sci. Volume 7, Number 1 (1992), 69-90.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
http://projecteuclid.org/euclid.ss/1177011444
Digital Object Identifier
doi:10.1214/ss/1177011444
Mathematical Reviews number (MathSciNet)
MR1173418
Zentralblatt MATH identifier
0955.62520
JSTOR
links.jstor.org
Keywords
Dynamical systems ergodic theory nonlinear time series stationary processes prediction
Citation
Berliner, L. Mark. Statistics, Probability and Chaos. Statist. Sci. 7 (1992), no. 1, 69--90. doi:10.1214/ss/1177011444. http://projecteuclid.org/euclid.ss/1177011444.
See also
- See Comment: Colleen D. Cutler. [Statistics, Probability and Chaos]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 91--94.Project Euclid: euclid.ss/1177011445
- See Comment: John Geweke. [Statistics, Probability and Chaos]: Comment: Inference and Prediction in the Presence of Uncertainty and Determinism. Statist. Sci., Volume 7, Number 1 (1992), 94--101.Project Euclid: euclid.ss/1177011446
- See Comment: Clive W. J. Granger. [Statistics, Probability and Chaos]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 102--104.Project Euclid: euclid.ss/1177011447
- See Comment: David Griffeath. [Statistics, Probability and Chaos]: Comment: Randomness in Complex Systems. Statist. Sci., Volume 7, Number 1 (1992), 104--108.Project Euclid: euclid.ss/1177011448
- See Comment: Richard L. Smith. [Statistics, Probability and Chaos]: Comment: Relation Between Statistics and Chaos. Statist. Sci., Volume 7, Number 1 (1992), 109--113.Project Euclid: euclid.ss/1177011449
- See Comment: Ruey S. Tsay. [Statistics, Probability and Chaos]: Comment: Simplicity and Nonlinearity. Statist. Sci., Volume 7, Number 1 (1992), 113--114.Project Euclid: euclid.ss/1177011450
- See Comment: Sangit Chatterjee, Mustafa R. Yilmaz. [Statistics, Probability and Chaos]: Rejoinder (Part 1). Statist. Sci., Volume 7, Number 1 (1992), 114--117.Project Euclid: euclid.ss/1177011451
- See Comment: L. Mark Berliner. [Statistics, Probability and Chaos]: Rejoinder (Part 2). Statist. Sci., Volume 7, Number 1 (1992), 118--122.Project Euclid: euclid.ss/1177011452
