Statistical Science

Statistics, Probability and Chaos

L. Mark Berliner

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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
https://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. https://projecteuclid.org/euclid.ss/1177011444


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See also

  • See Comment: Colleen D. Cutler. [Statistics, Probability and Chaos]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 91--94.
  • 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.
  • See Comment: Clive W. J. Granger. [Statistics, Probability and Chaos]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 102--104.
  • See Comment: David Griffeath. [Statistics, Probability and Chaos]: Comment: Randomness in Complex Systems. Statist. Sci., Volume 7, Number 1 (1992), 104--108.
  • See Comment: Richard L. Smith. [Statistics, Probability and Chaos]: Comment: Relation Between Statistics and Chaos. Statist. Sci., Volume 7, Number 1 (1992), 109--113.
  • See Comment: Ruey S. Tsay. [Statistics, Probability and Chaos]: Comment: Simplicity and Nonlinearity. Statist. Sci., Volume 7, Number 1 (1992), 113--114.
  • See Comment: Sangit Chatterjee, Mustafa R. Yilmaz. [Statistics, Probability and Chaos]: Rejoinder (Part 1). Statist. Sci., Volume 7, Number 1 (1992), 114--117.
  • See Comment: L. Mark Berliner. [Statistics, Probability and Chaos]: Rejoinder (Part 2). Statist. Sci., Volume 7, Number 1 (1992), 118--122.