Statistics 36-462: Chaos, Complexity, and Inference
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
emergence; heavy-tailed and "scale-free"
agents; and inference from simulations.
Textbooks: Gary William
Computational Beauty of Nature,
and John Miller
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.
See also the detailed syllabus with links to readings.
- 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
Page created 6 November 2007; last modified 6 January 2008