Cosma Shalizi

Statistics 36-462: Chaos, Complexity, and Inference

Spring 2008

TuTh 12:00-1:20, in 208 Scaife Hall
This course will cover some key parts of modern theories of nonlinear dynamics ("chaos") and complex systems, and their connections to fundamental aspects of probability and statistics. By studying systems with many strongly-interacting components, students will learn how stochastic models can illuminate phenomena beyond the usual linear/Gaussian/independent realm, as well as gain a deeper understanding of why stochastic models work at all.

The course will emphasize building modeling skill and intuition over rigor, though relevant mathematical results will be presented where applicable and accessible. Students will gain experience using, interpreting and designing simulation models of complex stochastic systems, understanding their varieties and limitations, and learn how to relate them to real-world data.

Topics will include: chaos theory and nonlinear prediction; information; the distinction between randomness and determinism; self-organization and emergence; heavy-tailed and "scale-free" distributions; complex networks; interacting agents; and inference from simulations.

Required Textbooks: Gary William Flake, The Computational Beauty of Nature, and John Miller and Scott Page, Complex Adaptive Systems.
Optional Textbook: Peter Guttorp, Stochastic Modeling of Scientific Data.

Prerequisites: A previous course in mathematical statistics (such as 36-310, 36-401, or 36-625/626) and a course in probability and random processes (such as 36-217, 36-225/226, 36-410, or 36-625/626); or consent of instructor. Some programming experience will be helpful.


Dynamical Systems: Jan. 15--Feb. 7
Dynamical systems, chaos, state-space reconstruction, prediction, information, inference for dynamical systems, and the relationship betwen randomness and determinism
Self-organization: Feb. 12--Feb. 21
Self-organizing systems, cellular automata
Heavy-tailed Distributions: Feb. 26--Mar. 6
Examples, properties, origins, estimation, testing
Inference from Simulations: Mar. 18--Mar. 27
Error statistics and severity; breaking your simulations; Monte Carlo, direct inference, parametric bootstrapping; indirect inference
Complex Networks and Agent-Based Models: Apr. 1--Apr. 29
Network structures and properties; network growth; agent-based modeling; collective phenomena; contagion on networks; network inference; social complexity; real-world examples
Chaos, Complexity and Inference: May 1
See also the detailed syllabus with links to readings.

Page created 6 November 2007; last modified 6 January 2008