Quantifying Uncertainty

Syllabus

Course Meeting Times

Lectures: 1 session / week, 2 hours / session

Prerequisites

Permission of instructor.

Objectives

• To understand the methods by which we can represent, propagate and infer uncertainty.
• To explore “interdisciplinary” application.
• To build an intellectual community around uncertainty quantification.

Topics Covered

The specific topics vary between offerings, but are generally drawn from the following:

• Density Estimation: Exponential Family, Mixture Models, Kernels, Markov Chain Monte Carlo
• Model Selection: Jacknife, Bootstrap, Cross-validation and Information Criteria
• Dimensionality Reduction: PCA, ICA, and other nonlinear modes
• Model Reduction: POD / EOF, Krylov, Response Surface Models, Polynomial Chaos
• Inference: Hierarchical Bayes, Graphical Models
• Time-dependent Inference: Linear, Ensemble, Mixture, Kernel, Mutual Information, and Particle Filtering and Smoothing
• Statistical Models: Regression Machines, Gaussian Processes, Markov Models
• Manifold Learning
• Information Theoretic Estimation, Control and Learning

Expectations

• Attend class.
• Read the assigned papers/readings.
• Every participant “recites” a paper.
• Do a project.
  • Use a method studied here in your application.
  • Develop a new method for applications studied here.
  • Write a review paper in a subject area.

General References

Bryson, Jr. Arthur E. and Yu-Chi Ho. Applied Optimal Control: Optimization, Estimation and Control. Taylor & Francis, 1975. ISBN: 9780891162285.

Gelb, Arthur. Applied Optimal Estimation. MIT Press, 1974. ISBN: 9780262570480.

Gelman, A., J. Carlin, et al. Bayesian Data Analysis. Chapman and Hall, 2003. ISBN: 9781584883883.

Martinez, W. L., and A. R. Martinez. Computational Statistics Handbook with MATLAB. 2nd ed. Chapman and Hall/CRC, 2007. ISBN: 978158488566. [Preview with Google Books]

Papoulis, A. Probability, Random Variables & Stochastic Processes. McGraw-Hill, 2002. ISBN: 9780071226615.

Silverman, B. W. Density Estimation for Statistics and Data Analysis. Chapman and Hall/CRC, 1986. ISBN: 9780412246203.

Double Pendulum.

Grading

The course grade is based upon paper explanation, project, and class participation.